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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

A particle is moving along a straight line such that its position is defined by s = (102 +20) mm, where t is in seconds. Determine (a) The displacement of the particleduring the time interval
A particle moves along a straight path with an acceleration of a = (5/s) m/s2, where s is in meters. Determine the particle’s velocity when s = 2 m, if it is released from rest when s = 1 m.
A particle moves along a straight line with an acceleration of a = 5/(3s¹/3 + 5/2) m/s², where s is in meters. Determine the particle's velocity when s = 2 m, if it starts from rest when s = 1 m.
A particle travels along a straight-line path such that in 4 s it moves from an initial position sA = -8 m to a position sB = +3 m. T hen in another 5 s it moves from sB to sC = -6 m. Determine the
The rider begins to apply a force to the rear wheel of his bicycle, thereby initiating an acceleration. If his velocity is described by the v-s graph, construct the a-s graph for the same interval. v
The dragster starts from rest and has a velocity described by the graph. Construct the s-t graph during the time interval 0 ≤ t ≤ 15 s. Also, determine the total distance traveled during this
The sports car starts from rest and travels along a straight road. Its initial increasing acceleration is caused by the rear wheels of the car as shown on the graph. Construct the v-s graph. What is
Car B is traveling a distance d ahead of car A. Both cars are traveling at 60 ft/s when the driver of B suddenly applies the brakes, causing his car to decelerate at 12 ft/s². It takes the driver of
The speed of a particle traveling along a straight line within a liquid is measured as a function of its position as v = (100 - s) mm/s, where s is in millimeters. Determine (a) The particle’s
The box slides down the path described by theequation y = (0.05x²) m, where x is in meters. If the box hasx components of velocity and acceleration of vx, = -3 m/sand ax = -1.5 m/s² at x = 5 m,
Car A starts from rest at t = 0 and travels along a straight road with a constant acceleration of 6 ft/s² until it reaches a speed of 80 ft/s. Afterwards it maintains this speed. Also, when t = 0,
Tests reveal that a driver takes about 0.75 s before he or she can react to a situation to avoid a collision. It takes about 3 s for a driver having 0.1% alcohol in his system to do the same. If such
The sports car travels along the straight road such that v = 3√2100-s m/s, where s is in meters. Determine the time for the car to reach s = 60 m. How much time does it take to stop?
The acceleration of the boat is defined by a = (1.5 v1/2) m/s. Determine its speed when t = 4 s if it has a speed of 3 m/s when t = 0.
A ball is released from the bottom of an elevator which is traveling upward with a velocity of 6ft/s. If the ball strikes the bottom of the elevator shaft in 3 s, determine the height of the elevator
A particle is moving along a straight line with an initial velocity of 6 m/s when it is subjected to a deceleration of a = (-1.5v1/2) m/s2, where v is in m/s. Determine how far it travels before it
A freight train travels at v = 60(1 - e-t) ft/s, where t is the elapsed time in seconds. Determine the distance traveled in three seconds, and the acceleration at this time. sm
A particle moves along a straight path with an acceleration of a = (kt³+4) ft/s², where t is in seconds. Determine the constant k, knowing that v = 12 ft/s when t = 1 s, and that v=-2 ft/s when t =
The velocity of a particle traveling along a straight line is v = (3t²- 6t) ft/s, where t is in seconds. If s = 4 ft when t = 0, determine the position of the particle when t = 4 s. What is the
Determine the speed at which the basketball at A must be thrown at the angle of 30° so that it makes it to the basket at B. 30° -X 1.5 m -10 m- B 3m
A particle is moving along a straight line such that its acceleration is defined as a = (-2v) m/s2, where v is in meters per second. If v = 20 m/s when s = 0 and t = 0, determine the particle’s
When a particle is projected vertically upward with an initial velocity of v0, it experiences an accelerationa = -(g + kv²), where g is the acceleration due to gravity,k is a constant, and is the
If the car decelerates uniformly along the curved road from 25 m/s at A to 15 m/s at C, determine the acceleration of the car at B. 250 m PB = 300 m 50 m
The boat is traveling along the circular path with a speed of v= (0.0625t2) m/s, where t is in seconds.Determine the magnitude of its acceleration when t = 10 s. 40 m -v = 0.0625f²
When x = 10 ft, the crate has a speed of 20 ft/s which is increasing at 6 ft/s². Determine the direction of the crate's velocity and the magnitude of its acceleration at this instant. 20
When a particle falls through the air, its initial acceleration a = g diminishes until it is zero, and thereafter it falls at a constant or terminal velocity vf. If this variation of the acceleration
A train is initially traveling along a straight track at a speed of 90 km/h. For 6 s it is subjected to a constant deceleration of 0.5 m/s2, and then for the next 5 s it has a constant deceleration
Two cars A and B start from rest at a stop line. Car A has a constant acceleration of aA = 8 m/s2, while car B has an acceleration of aB = (2t3/2) m/s2, where t is in seconds. Determine the distance
A sphere is fired downward into a medium with an initial speed of 27 m/s. If it experiences a deceleration of a = (-6t) m/s², where t is in seconds, determine the distance traveled before it stops.
Peg P is driven by the fork link OA along the curved path described by r= (2θ) ft. At the instant 0 = π/4 rad, the angular velocity and angular acceleration of the link are θ́ = 3 rad/s and θ̈
The s-t graph for a train has been experimentally determined. From the data, construct the v-t and a-t graphs for the motion; 0 ≤ t ≤ 40 s. For 0 ≤ t < 30 s, the curve is s = (0.41²) m, and
A freight train starts from rest and travels with a constant acceleration of 0.5 ft/s². After a time t' it maintains a constant speed so that when t = 160 s it has traveled 2000 ft. Determine the
Water is sprayed at an angle of 90° from the slope at 20 m/s. Determine the range R. R VB = 20 m/s
If the effects of atmospheric resistance are accounted for, a freely falling body has an acceleration defined by the equation, a = 9.81[1- v²(10-4)] m/s², where v is in m/s and the positive
A ball is thrown with an upward velocity of 5 m/s from the top of a 10-m-high building. One second later another ball is thrown upward from the ground with a velocity of 10 m/s. Determine the height
The platform is rotating about the vertical axis such that at any instant its angular position is = (4/³/2) rad,where t is in seconds. A ball rolls outward along the radialgroove so that its
The car travels up the hill with a speed of v = (0.2s) m/s, where s is in meters, measured from A. Determine the magnitude of its acceleration when it is at s = 50 m, where ρ = 500 m. A s = 50
The car has a speed of 55 ft/s. Determine the angular velocity θ of the radial line OA at this instant. Ox r = 400 ft COMO A
A particle is moving along a straight line such that its position is given by s= (4t - t2) ft, where t is in seconds.Determine the distance traveled from t = 0 to t = 5 s, theaverage velocity, and
Ball A is thrown vertically upward from the top of a 30-m- high building with an initial velocity of 5 m/s. At the same instant another ball B is thrown upward from the ground with an initial
As a body is projected to a high altitude above the earth's surface, the variation of the acceleration of gravity with respect to altitude y must be taken into account. Neglecting air resistance,
The elevator starts from rest at the first floor of the building. It can accelerate at 5 ft/s² and then decelerate at 2 ft/s². Determine the shortest time it takes to reach a floor 40 ft above the
Accounting for the variation of gravitational acceleration a with respect to altitude y (see Prob. 12–33), derive an equation that relates the velocity of a freely falling particle to its altitude.
A car starting from rest moves along a straight track with an acceleration as shown. Determine the time t for the car to reach a speed of 50 m/s and construct the v–t graph that describes the
Two rockets start from rest at the same elevation. Rocket A accelerates vertically at 20 m/s2 for 12 s and then maintains a constant speed. Rocket B accelerates at 15 m/s2 until reaching a constant
The motion of a jet plane just after landing on a runway is described by the a–t graph. Determine the time t when the jet plane stops. Construct the v–t and s–t graphs for the motion. Here s =
A particle starts from s = 0 and travels along a straight line with a velocity v = (t²- 4t+ 3) m/s, where t is in seconds. Construct the v-t and a-t graphs for the time interval 0 ≤ t ≤ 4 s.
The v-t graph for a particle moving through an electric field from one plate to another has the shape shown in the figure. The acceleration and deceleration that occur are constant and both have a
If the position of a particle is defined by s = [2 sin (π/5)t + 4] m, where t is in seconds, constructthe s-t, v-t, and a-t graphs for 0 ≤ t ≤ 10 s.
An airplane starts from rest, travels 5000 ft down a runway, and after uniform acceleration, takes off with a speed of 162 mi/h. It then climbs in a straight line with a uniform acceleration of 3
Car A is traveling with a constant speed of 80 km/h due north, while car B is traveling with a constant speed of 100 km/h due east. Determine the velocity of car B relative to car A. FORD B 100
The v–t graph for a particle moving through an electric field from one plate to another has the shape shown in the figure, where t' = 0.2 s and vmax = 10 m/s. Draw the s–t and a–t graphs for
Two planes A and B are traveling with the constant velocities shown. Determine the magnitude and direction of the velocity of B relative to A. Ug = 800 km/h VA = 650 km/h B 60°
The a–s graph for a rocket moving along a straight track has been experimentally determined. If the rocket starts at s = 0 when v = 0, determine its speed when it is at s = 75 ft, and 125 ft,
The boats A and B travel with constant speeds of VA = 15 m/s and VB = 10 m/s when they leave the pier at O at the same time. Determine the distance between them when t = 4 s. У UB = 10
The rocket has an acceleration described by the graph. If it starts from rest, construct the v-t and s-t graphs for the motion for the time interval 0 ≤ t ≤ 14s. a(m/s²) 38 18. a² = 36t a = 4t
The s–t graph for a train has been determined experimentally. From the data, construct the v–t and a–t graphs for the motion. s (m) 600 360 s 24t360- s = 0.41² 30 40 Hote -t (s)
The jet car is originally traveling at a velocity of 10 m/s when it is subjected to the acceleration shown. Determine the car’s maximum velocity and the time t when it stops. When t = 0, s = 0. a
From experimental data, the motion of a jet plane while traveling along a runway is defined by the v–t graph shown. Construct the s–t and a–t graphs for the motion. v (m/s) 80 10 40 -t (s)
The v-t graph for a train has been experimentally determined. From the data, construct the s-t and a-t graphs for the motion for 0 ≤ t ≤ 180 s. When t=0,s=0. v (m/s) 10 6 60 120 180 ... ... t (s)
An airplane lands on the straight runway, originally traveling at 110 ft/s when s = 0. If it is subjected to the decelerations shown, determine the time t' needed to stop the plane and construct the
Starting from rest at s = 0, a boat travels in a straight line with the acceleration shown by the a-s graph. Determine the boat's speed when s = 50 ft, 100 ft, and 150 ft. a (ft/s²) 8 6 100 150 -s
A motorcycle starts from rest at s = 0 and travels along a straight road with the speed shown by the v–t graph. Determine the total distance the motorcycle travels until it stops when t = 15 s.
A motorcycle starts from rest at s = 0 and travels along a straight road with the speed shown by the v–t graph. Determine the motorcycle’s acceleration and position when t = 8 s and t = 12 s. v
Starting from rest at s = 0, a boat travels in a straight line with the acceleration shown by the a–s graph. Construct the v–s graph. a (ft/s²) 100 150 s (ft)
The v–t graph for the motion of a car as it moves along a straight road is shown. Draw the s–t and a–t graphs. Also determine the average speed and the distance traveled for the 15-s time
The speed of a train during the first minute has been recorded as follows:Plot the v-t graph, approximating the curve as straight-line segments between the given points. Determine the total distance
A motorcyclist starting from rest travels along a straight road and for 10 s has an acceleration as shown. Draw the v-t graph that describes the motion and find the distance traveled in 10 s. a
The boat is originally traveling at a speed of 8 m/s when it is subjected to the acceleration shown in the graph. Determine the boat’s maximum speed and the time t when it stops. - t(s) 1 24 9 +
The v - s graph of a cyclist traveling along a straight road is shown. Construct the a-s graph. v (ft/s) 15-- v= 0.1s + 5. 5- 100 v=-0.04s + 19 350 S (ft)
The jet bike is moving along a straight road with the speed described by the v-s graph. Construct the a-s graph. v(m/s) 75. 15- v = 55¹/2 225 -v = -0.2s + 120 525 s(m)
The a–s graph for a freight train is given for the first 200 m of its motion. Plot the v–s graph. The train starts from rest. a (m/s?) 2 100 200 -s(m)
A man riding upward in a freight elevator accidentally drops a package off the elevator when it is 100 ft from the ground. If the elevator maintains a constant upward speed of 4 ft/s, determine how
Two cars start from rest side by side and travel along a straight road. Car A accelerates at 4 m/s² for 10 s and then maintains a constant speed. Car B accelerates at 5 m/s² until reaching a
The jet plane starts from rest at s = 0 and is subjected to the acceleration shown. Construct the v–s graph and determine the time needed to travel 500 ft down the runway. a (ft/s²) 75 a = 75
The water sprinkler, positioned at the base of a hill, releases a stream of water with a velocity of 15 ft/s as shown. Determine the point B(x, y) where the water strikes the ground on the hill.
If the position of a particle is defined as S = (5t - 31²) ft, where t is in seconds, construct the s-t, v-t, and a-t graphs for 0 ≤ t ≤ 2.5s.
A particle travels along the curve from A to B in 5 s. It takes 8 s for it to go from B to C and then 10 s to go from C to A. Determine its average speed when it goes around the closed path. y A 20
A rocket is fired from rest at x = 0 and travels along a parabolic trajectory described by y2 = [120(103)x] m. If the x component of acceleration iswhere t is in seconds,determine the magnitudes of
A particle travels along the curve from A to B in 2 s. It takes 4 s for it to go from B to C and then 3 s to go from C to D. Determine its average speed when it goes from A to D. y A 10 m B 15 m. C 5
If the velocity of a particle is defined as v(t) = {0.8t2i + 12t1/2j + 5k} m/s, determine the magnitude and coordinate direction angles α, β, γ of the particle’s acceleration when t = 2 s.
A particle moves along the curve y = e2x such that its velocity has a constant magnitude of v = 4 ft/s. Determine the x and y components of velocity when the particle is at y = 5 ft.
A particle travels along the parabolic path y = bx². If its component of velocity along the y axis is vy, = ct², determinethe x and y components of the particle's acceleration. Here band c are
A car traveling along the road has the velocities indicated in the figure when it arrives at points A, B, and C. If it takes 10 s to go from A to B, and then 15 s to go from B to C, determine the
A particle travels along the circular path x2 + y2 = r2. If the y component of the particle’s velocity is vy = 2r cos 2t, determine the x and y components of its acceleration at any instant.
The particle travels along the path defined by the parabola y = 0.5x². If the component of velocity along the x axis is vx = (5t) ft/s, where t is in seconds, determine the particle's distance from
A particle moves along the curve y = x - (x2/400), where x and y are in ft. If the velocity component in the x direction is vx = 2 ft/s and remains constant, determine the magnitudes of the velocity
The motorcycle travels with constant speed v0 along the path that, for a short distance, takes the form of a sine curve. Determine the x and y components of its velocity at any instant on the curve.
The roller coaster car travels down the helical path at constant speed such that the parametric equations that define its position are x = c sin kt, y = c cos kt, z = h − bt, where c, h, and b are
Show that if a projectile is fired at an angle from the horizontal with an initial velocity v0, the maximum rangethe projectile can travel is given by Rmax = v02/g, where g isthe acceleration of
Pegs A and B are restricted to move in the elliptical slots due to the motion of the slotted link. If the link moves with a constant speed of 10 m/s, determine the magnitudes of the velocity and
The van travels over the hill described by y = (-1.5(10-³) x² +15) ft. If it has a constant speed of75 ft/s, determine the x and y components of the van'svelocity and acceleration when x = 50ft. 15
The flight path of the helicopter as it takes off from A is defined by the parametric equations x = (2t²) m and y = (0.04t³) m, where t is the time in seconds. Determine the distance the helicopter
Determine the minimum initial velocity v0 and the corresponding angle θ0 at which the ball must be kicked in order for it to just cross over the 3-m-high fence. 6 m 3 m
The catapult is used to launch a ball such that it strikes the wall of the building at the maximum height of its trajectory. If it takes 1.5 s to travel from A to B, determine the velocity vA at
Neglecting the size of the ball, determine the magnitude vA of the basketball’s initial velocity and its velocity when it passes through the basket. 30% A 2 m -10 m- B ww 3 m
Show that the girl at A can throw the ball to the boy at B by launching it at equal angles measured up or down from a 45° inclination. If vA = 10 m/s, determine the range R if this value is 15°,
The girl at A can throw a ball at vA= 10 m/s. Calculate themaximum possible range R = Rmax and the associated angle θ at which it should be thrown. Assume the ball is caught at B at the same
The ball at A is kicked with a speed vA = 16 ft/s and at an angle θA = 30°. Determine the point (x, –y) where it strikes the ground. Assume the ground has the shape of a parabola as shown.
The ball at A is kicked such that θA = 30°. If it strikes the ground at B having coordinates x = 15 ft, y = -9 ft, determine the speed at which it is kicked and the speed at which it strikes the

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