Question

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 18.0m/s , and the distance between them is 54.0m. (A) 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 t2-t1. (B) How far does the motorcycle travel from the moment it starts to accelerate (at time t1) until it catches up with the car (at time t2)? Should you need to use an answer from a previous part, make sure you use the unrounded value

Answer 1

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

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 at the same speed of 22.5m/s and the distance between them is 57.0m. After t1 = 5.00s the motorcycle starts to accelerate at a rate of 7.00m/s2 The motorcycle catches up with car at some time t2. 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 t2 - t1. Express the time numerically in seconds using three significant figures. How far does the motorcycle tracel form the moment it starts to accelerate (at time t1) until it catches up with the car (at time t2)? Should you need to use an answer from a previous part. make sure you use the unrounded value.

Till the time t1, the distance betwen them remains 57m as both are traveeling with same speed.

Let, t2 - t1 = T

Here, acceleration = 7 m/s^2

Extra Distance to cover = 57 m

1/2 * a * T^2 = 57

T^2 = 57*2/7

Thus, T = 4.04 s

Distance travelled by motor cyclist, s = ut + 57 = 22.5*4.04 + 57 = 147.9 m