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Question

If the speed of a particle is given as v=3t2+5 m/s, the speed of the particle at 4 sec and the average speed in 4 sec respectively is

A
53 m/s,84 m/s
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B
53 m/s,21 m/s
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C
50 m/s,21 m/s
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D
45 m/s,20 m/s
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Solution

The correct option is B 53 m/s,21 m/s
Given, speed of the particle as v(t)=3t2+5
So, the speed of the particle at t=4 sec, is given as
v(t=4 sec)=3×42+5=53 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)=3t2+5
and, distance =t0v(t)dt
S=40(3t2+5)dt=[t3+5t]40
S=(43+5×4)(0+0)=84 m
Thus, average speed of the car is 844=21 m/s

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