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 18.0m/s , and the distance between them is 54.0m. 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.

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

Explanation / Answer

I would approach it this way.
Since the acceleration is constant, the average velocity is 1/2 of the speed after accelerating.
And the motorcycle has to cover 54 m..
So we call the time to catch up as T.
Average velocity = 54/T
And average velocity = 1/2 x 7 x T.
54/T = 1/2 x 7 x T.
So T^2 = 54/3.5
T = 3.928.

So that's how long it took to catch up. t2 = 4+3.928.

As for distance covered
You know it started at 18.
After accelerating it was going 18+Tx7
Average velocity as the average of those two values.
Distance covered is the average velocity times T

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