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Question

If the speed of a particle is given as v=6t2+2t+5 m/s, the speed of the particle at 4 sec and the average speed in 4 sec respectively is

A
100 m/s,40 m/s
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B
120 m/s,50 m/s
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C
109 m/s,41 m/s
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D
109 m/s,164 m/s
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Solution

The correct option is C 109 m/s,41 m/s
Given, speed of the particle as v(t)=6t2+2t+5
So, the speed of the particle at t=4 sec, is given as
v(t=4 sec)=6×42+2×4+5=109 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+5
and, distance =t0v(t)dt
S=40(6t2+2t+5)dt=[2t3+t2+5t]40
S=(2×43+42+5×4)(0+0)=164 m
Thus, average speed of the car is 1644=41 m/s

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