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 19.0m/s , and the distance between them is 52.0m . After t1 = 5.00s , the motorcycle starts to accelerate at a rate of 5.00m/s^2. How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car?

Answer 1

4.56 s

Step-by-step explanation:

Answer 2

4.56 s

Step-by-step explanation:

Let t (seconds) be the time it takes from the moment when the motorcycle starts to accelerate until it catches up with the car. Since prior to this they are traveling at constant speed, they would have maintained a distance of 52 m before accelerating.

The distance traveled by the car, with respect the motorcycle position when it start accelerating is

`s_c = s_0 + v_ct = 52 + 19t`

The distance traveled by the motorcycle after accelerating, with respect the motorcycle position when it start accelerating is

`s_m = v_mt + at^2/2 = 19t + 5t^2/2`

When the motorcycle catches up to the car, their position are at the same

`s_c = s_m`

`52 + 19t = 19t + 5t^2/2`

`52 = 5t^2/2`

`t^2 = 20.8`

`t = √(20.8) = 4.56 s`