Question

A motorcycle is following a car that is traveling at a constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 19.0 m/s, and the distance between them is 52.0 m. After t1 = 5.00 s, the motorcycle starts to accelerate at a rate of 5.00 m/s2. How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car?

Answer 1

t=2.14s

Step-by-step explanation:

Since it asks us for the time it takes from the moment it starts accelerating, the first 5 seconds of movement mentioned is irrelevant here.

Next it'd be simple just to use the kinematic equation involving distance, time, and velocity:

∆d=V₀t+at²/2

From here we can move the change in distance over and use the quadratic formula to solve for time.

My work is in the attachment. Comment with any questions.