Question

A car is traveling at a steady 71 km/r in a 50 km/h zone. A police motorcycle takes off at the instant the car passes it, accelerating at a steady 7.2 m/s².

Part A

How much time elapses before the motorcycle is moving as fast as the car?

Part B

How far is the motorcycle from the car when it reaches this speed?

Answer 1

here,

speed of car , u = 71 km/h

u = 19.72 m/s

accelration of police motorcycle , a = 7.2 m/s^2

part A

let the time elapses before the motorcycle is moving as fast as the car be t

initial speed of motorcycle , um = 0

using first equation of motion

v = u + a *t

19.72 = 0 + 7.2 *a

t = 2.74 s

the time elapses before the motorcycle is moving as fast as the car is 2.74 s

part B

the motorcycle distance covered it reaches this speed be s

using seccond equation of motion

s = u*t + 0.5 * a*t^2

s = 0 + 0.5 *7.2*2.74^2

s = 27.03 m

the motorcycle distance from the car when it reaches this speed , d = u *t - s

d = 19.72*2.74 - 27.03

d = 27.01 m

the motorcycle distance from the car when it reaches this speed is 27.01 m