FINAL REVIEW #$1$

$1.$ By analyzing the x$-$t graph shown here, answer the questions below. The first segment of the graph has a width of $5$ seconds and a height of $7$ m$.$ The width of the middle segment of the graph is $6$ seconds. The final segment of the graph has a width of $3$ seconds.

a$.$ Create an accurate v$-$t graph that expresses the same motion. b$.$ What is the velocity of the object during the first $5$ seconds? c$.$ What is the average velocity of the object over the entire

experiment?

d$.$ What is the average speed of the object over the entire

experiment?

e$.$ What is the average velocity during the final three seconds?

f$.$ What is the total area under the v$-$t graph you created? How does that answer correlate

to the x$-$t graph?

$2.$ By analyzing the v$-$t graph shown here, answer the questions below. The initial velocity on the graph is $10$ m$/$s forward. It takes $8$ seconds for the object to come to rest $($momentarily$.)$ The object moves backward for an additional $2$ seconds until it reaches a final velocity of $2\mathrm{.}5$ m$/$s backward.

a$.$ How far does the object move in the first $8$ seconds?

b$.$ If the initial position of the object was at x $=-15$ meters, what

it the final position?

c$.$ What is the acceleration of this object?

$3.$ Consider the motion of the horse in the sketch below. During the first $10$ seconds the horse moved with constant speed. During the next $10$ seconds the horse accelerated uniformly. During the final $20$ seconds the horse underwent a different uniform acceleration. Create a motion graph $($position vs$.$ time$)$ for the horse.

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Dr$.$ Tehseen Adel PHYS$-250$

If this is being turned in for extra credit, you must show all work, diagrams, and equations for maximum points possible $($graded for accuracy$).$ Electronic submissions will be accepted. You may submit portions of this for partial extra credit. You may use any resources available to you to answer these questions. The final date to turn this document for extra credit is December $9,2024.$

$4.$ A skydiver is falling with speed v$0$ through the air. At that moment $($time t $=0),$ she opens her parachute and experiences the force of air resistance whose strength is given by the equation: F $=$ kv$,$ in which k is a proportionality constant and v is her descent speed. The total mass of the skydiver and equipment is m$.$ Assume that g is constant throughout her descent.

a$.$ Draw and label all the forces acting on the skydiver after her parachute opens.

b$.$ Determine the skydiver$$s acceleration in terms of m$,$ v$,$ k$,$ and g$.$

c$.$ Determine the skydiver$$s terminal velocity $($that is$,$ the eventual constant speed of

descent$).$ Explain how the force of gravity acting on the skydiver compares to the total air resistance acting on the skydiver after terminal velocity is reached.

$5.$ Zach whose mass is $80$ kg is in an elevator descending at $10$ m$/$s$.$ The elevator takes $3\mathrm{.}0$ s to brake to stop at the first floor.

a$.$ What is Zach$$s apparent weight before the elevator starts braking? b$.$ What is Zach$$s apparent weight while the elevator is braking?

$6.$ A crate of mass $31\mathrm{.}0$ kg is pulled over the floor with a force of $275$ N$.$ The force makes an angle of $24\mathrm{.}0$ with the horizontal. Assuming there is no friction between the crate and the floor, find the resultant force acting on the crate, the acceleration of the crate, and the magnitude of the normal force.

$7.$ You throw a stone horizontally at a speed of $5\mathrm{.}0$ m$/$s from the top of a cliff that is $78\mathrm{.}4$ m high. a$.$ How long does it take the stone to reach the bottom of the cliff?

b$.$ How far from the base of the cliff does the stone hit the ground?

c$.$ What are the horizontal and vertical components of the stone$$s velocity just before it

hits the ground?

$8.$ On an airless planet the same size and mass of the Earth, Jim and Sara stand at the edge of a $50$ m high cliff. Jim extends his arm over the cliff edge and throws a ball straight up with an initial speed

a$.$ Create an accurate v$-$t graph that expresses the same motion. b$.$ What is the velocity of the object during the first $5$ seconds? c$.$ What is the average velocity of the object over the entire

experiment?

d$.$ What is the average speed of the object over the entire

experiment?

e$.$ What is the average velocity during the final three seconds?

f$.$ What is the total area under the v$-$t graph you created? How does that answer correlate

to the x$-$t graph?

a$.$ Create an accurate v$-$t graph that expresses the same motion. b$.$ What is the velocity of the object during the first $5$ seconds? c$.$ What is the average velocity of the object over the entire

experiment?

d$.$ What is the average speed of the object over the entire

experiment?

e$.$ What is the average velocity during the final three seconds?

f$.$ What is the total area under the v$-$t graph you created? How does that answer correlate

to the x$-$t graph?