Goal Apply kinematics to horizontal motion with two phases. hs SOLUTION Problem A typical jetliner lands...

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Goal Apply kinematics to horizontal motion with two phases. hs SOLUTION Problem A typical jetliner lands at a speed of 160 mi/h and decelerates at the rate of (10 mi/h)/s. If the plane travels at a constant speed of 160 mi/h for 1.0 s after landing before applying the brakes, what is the total displacement of the aircraft between touchdown on the runway and coming to rest? Convert units of speed and acceleration to SI. Taking a = 0, y = 71.5 m/s, and t = 1.00 s, find the displacement while the plane is coasting. Use the time-independent kinematic equation to find the displacement while the plane is braking, Take a = -4.47 m/s and 10 = 71.5 m/s. The negative sign on a means that the plane is slowing down. Sum the two results to find the total displacement. LEARN MORE Origin Strategy First, convert all quantities to SI units. The problem must be solved in two parts, or phases, corresponding to the initial coast after touchdown, followed by braking. Using the kinematic equations, find the displacement during each part and add the two displacements. 2 MIK X How much extra distance dose the coasting distance %= 71.5 m/s 4-0 t=1.0 s Yo (160 mi/h) AX braking Coasting and braking distances for a landing jetliner. I v = y + 2ax braking braking distance V 70 = 71.5 m/s V, = 0 a = -4.47 m/s 2a a = (-10 (mi/h)/'s) ( .007 m) Axcoasting = Vot + /at = (71.5 m/s) (1.00 s) + 0 = 71.5 0.447 m/s 1.00 mi/h ) = 71.5 m/s 7 -4.47 m/s 0 (71.5 m/s) 2.00 (-4,47 m/s) 572 m Axcoasting Axbraking = 72 m +572 m = 644 m Remarks To find the displacement while braking, we could have used the two kinematics equations involving time, namely, Ax = vol + at and v = v + at, but because we weren't interested in time, the time-independent equation was easier to use. Question By how much would the answer change if the plane coasted for 2.0 s before the pilot applied the brakes? +x Goal Apply kinematics to horizontal motion with two phases. hs SOLUTION Problem A typical jetliner lands at a speed of 160 mi/h and decelerates at the rate of (10 mi/h)/s. If the plane travels at a constant speed of 160 mi/h for 1.0 s after landing before applying the brakes, what is the total displacement of the aircraft between touchdown on the runway and coming to rest? Convert units of speed and acceleration to SI. Taking a = 0, y = 71.5 m/s, and t = 1.00 s, find the displacement while the plane is coasting. Use the time-independent kinematic equation to find the displacement while the plane is braking, Take a = -4.47 m/s and 10 = 71.5 m/s. The negative sign on a means that the plane is slowing down. Sum the two results to find the total displacement. LEARN MORE Origin Strategy First, convert all quantities to SI units. The problem must be solved in two parts, or phases, corresponding to the initial coast after touchdown, followed by braking. Using the kinematic equations, find the displacement during each part and add the two displacements. 2 MIK X How much extra distance dose the coasting distance %= 71.5 m/s 4-0 t=1.0 s Yo (160 mi/h) AX braking Coasting and braking distances for a landing jetliner. I v = y + 2ax braking braking distance V 70 = 71.5 m/s V, = 0 a = -4.47 m/s 2a a = (-10 (mi/h)/'s) ( .007 m) Axcoasting = Vot + /at = (71.5 m/s) (1.00 s) + 0 = 71.5 0.447 m/s 1.00 mi/h ) = 71.5 m/s 7 -4.47 m/s 0 (71.5 m/s) 2.00 (-4,47 m/s) 572 m Axcoasting Axbraking = 72 m +572 m = 644 m Remarks To find the displacement while braking, we could have used the two kinematics equations involving time, namely, Ax = vol + at and v = v + at, but because we weren't interested in time, the time-independent equation was easier to use. Question By how much would the answer change if the plane coasted for 2.0 s before the pilot applied the brakes? +x