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 22.0 m/s , and the distance between them is 56.0 m . After t1 = 5.00 s , the motorcycle starts to accelerate at a rate of 8.00 m/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 t2t1.

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.

Explanation / Answer

s=56m, u=22m/s, a=8m/s2

s=ut +05at*t

v*v=u*u+2as     v*v=22*22+2*8*56=1380 v=sqrt 1380=37.15m/s

v=u+at    37.15=22+8t     t1=1.894s

t2=5+1.894 = 6.894m/s

t2= 6.894s Ans

for t1=5s,

distance covered=22*5=110m,

during the acceleration, u=ut+0.5a*t*t

=22*1.894+0.5*8*1.894*1.894

=56.02m.

total distance coverd=110+56.02=166.02m

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