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 54.0 m . After t1 = 4.00 s , the motorcycle starts to accelerate at a rate of 7.00 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.

Explanation / Answer

here,

A)

the graph A correctly displays the positions of the motorcycle and car as functions of time

B)

initial speed of both the cars and motorcycle , u = 19.5 m/s

and distance between them , di = 54 m

t1 = 4s

the accelration, a = 7 m/s^2

let the distance travelled be car be s and motorcycle takes t time to reach car

distance travelled by motorcycle , d = 54 + s

for car , s = 19.5 *t

using seccond equation of motion

s + 54 = 19.5 *t + 0.5 *7 *t^2

19.5 * t + 54 =    19.5 *t + 0.5 *7 *t^2

t = 3.93 s

time take from the moment when the motorcycle starts to accelerate until it catches up with the car is 3.93 s

c)

distance travelled by motorcycle be d

using seccond equation of motion

d = 19.5 *3.93 +54

d = 130.64 m

the distnace travelled by the motorcycle is 130.64 m

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