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Question

# A car starts from a point P at time t=0 sec and stops at point Q. The distance S, in meters,travelled by it in t sec is given by S=t2(2−t3). Which of the following(s) is/are true

A
Velocity at t=1 sec, is 3 m/sec
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B
Time taken to reach Q is 4 sec
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C
Distance between P and Q is 32 meters
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D
Acceleration at t=1 sec, is 2 m/sec2
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Solution

## The correct option is D Acceleration at t=1 sec, is 2 m/sec2Given : S=t2(2−t3)=2t2−t33 ⇒ velocity,V=dSdt=4t−t2⋯(1) ⇒ acceleration,a=dVdt=4−2t⋯(2) (a) At point Q,V=0⇒t(4−t)=0⇒t=0,4 So, car reaches at Q in t=4 sec (b) Distance between P and Q=32−643=323 meters (c) Acceleration,a(t=1)=4−2=2 m/sec2 (d) Velocity,V(t=1)=4−1=3 m/sec

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