A motorcycle is following a car that is traveling at constant speed on a straigh

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 20.5 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 4.00 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 (a 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

Let M = distance travelled by the motorcycle when it catches up with the car

M = 20.5(T2) + (1/2)(a)(T2)^2
M = 20.5(T2) + (1/2)(4)(T2)^2
M = 20.5(T2) + 2(T2)^2
Let C = distance travelled by the car when the motorcycle catches up with it

C = 20.5(T2)

When the motorcycle catches up with the car, then

M = 58 + C
Therefore, 20.5(T2) + 2(T2)^2 = 58 + 20.5(T2)

Since "20.5(T2)" appears on both sides of the equation, it will simply cancel out, hence the above equation is modified to

2(T2)^2 = 58
(T2)^2 = 58/2= 29 =T2 = 5.38 sec.

b) M = 20.5(T2) + 2(T2)^2
M = 20.5(5.38) + 2(5.38)^2
M = 168.18 m

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