I need help with both parts A Motorcycle Catches a Car A motorcycle is following

Question

I need help with both parts

A Motorcycle Catches a Car A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 23.0 m/s, and the distance between them is 58.0 m. After t_1 = 5.00 s, the motorcycle starts to accelerate at a rate of 5.00 m/s^2. The motorcycle catches up with the car at some time t_2. How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words, find t_2 - t_1. Express the time numerically in seconds using three significant figures. How far does the motorcycle travel from the moment it starts to accelerate (at time t_1) until it catches up with the car (at time t_2)? Should you need to use an answer from a previous part, make sure you use the unrounded value. Answer numerically in meters using three significant figures.

Explanation / Answer

PART A)

initial relative speed, u= 23-23 =0

relative acceleration, a = 5 m/s^2

relative distance, s = 58 m

using second equation of motion,

s = ut + 0.5at^2

58 =0+0.5*5t^2

t^2 = 2*58/5 =23.2

t = 4.82 s

Hence t2 - t1 = 4.82 s

part B)

using second equation of mottion,

s = ut +0.5at^2

   = 23*4.82 + 58

     = 169 m

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