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 21.5m/s , and the distance between them is 55.0m . After t1 = 5.00s , the motorcycle starts to accelerate at a rate of 8.00m/s2 . The motorcycle catches up with the car at some time t2.

A.)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

t2?t1.

B.) How far does the motorcycle travel from the moment it starts to accelerate (at time

Explanation / Answer

The displacement of car in t1 sec

D1 = x + u t1

D1 = 55 + (21.5 m/s ) t1

The displacement of motorcycle in t1 sec

D2 = u t1 + 1/2 a t1^2

D2 = 21.5 t1 + 1/2 a t1^2

D1 = D2

55 + (21.5 m/s ) t1 = 21.5 t1 + 1/2 a t1^2

t1 = sqrt [55 * 2 / 8 ]

t = t2- t1 = 3.71 s

-------------------------------------

Distance travelled by motor cycle

s= 55 + (21.5 * 3.71)

= 134.76 m

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