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Question

If the speed of a particle is given as v=6t2+2t m/s, the speed of the particle at 3 sec and the average speed in 4 sec respectively is

A
60 m/s,36 m/s
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B
54 m/s,36 m/s
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C
60 m/s,32 m/s
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D
60 m/s,30 m/s
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Solution

The correct option is A 60 m/s,36 m/s
Given, speed of the particle as v(t)=6t2+2t
So, the speed of the particle at t=3 sec, is given as
v(t=3 sec)=6×32+2×3=60 m/s

Now, average speed of the car is given by
Total distance covered (S)Total time taken (t)
Given, the speed of the car is v(t)=6t2+2t
and, distance =t0v(t)dt
S=40(6t2+2t)dt=[2t3+t2]40
S=(2×43+42)(0+0)=144 m
Thus, average speed of the car is 1444=36 m/s

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