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 19.5 m/s , and the distance between them is 57.0 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.

a) Which of the graphs (Figure 1)correctly displays the positions of the motorcycle and car as functions of time?

b) 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.

c) 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.

d)

Explanation / Answer

a) A represents the correct graph because constant slope of x- t means constant velocity

and increasing by curve x- t means const acceleration

b) let the distance travelled by car in t2-t1 time be x

so distance travelled by motor in t2-t1 time will be x + 57

also x/t = 19.5

so x = 19.5 t

and x + 57 = 19.5 t + 1/2 * 5 * t2

t = 4.77 seconds

so t2 = 9.77 sec

c) so distance travelled by motor in t2-t1 time will be x + 57

= 19.5 t + 57 = 150.11 m

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