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 23.0 m/s , and the distance between them is 58.0 m . After t1 = 5.00 s , the motorcycle starts to accelerate at a rate of 5.00 m/s2 . The motorcycle catches up with the 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 t2t1.

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

The speed of the car is constant, 23 m/s

the speed of the motorcycle is in the time t1=5 s, v1=23 m/s

The distance between them is 58 m, soif the motorcycle accelerate at 5 m/s^2.

If d1=0m is the point where the motocycle is at the time of t1=5 s, and d2=58 m is the point where the car is, d3 is gonna be the point where the motorcycle is gonna catch the car, at the time of t2, and d is the distance that both are gonna pass, so d3=58+d

so we use this:

d3-d1=vi*(t2-t1)+(1/2)*a*(t2-t1)^2 for the motorcycle and

d3-d2=vi*(t2-t1) for the car

58+d-0=23*(t2-5)+(1/2)*5*(t2-5)^2

58+d-58=23*(t2-5)

the value of t2 and d are

t2=9.81644 s

and d=110.783 m and this is all of the motorcycle traveled from time 1 to time 2

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