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Question

If velocity of a particle is v(t)=82t m/s, the average speed and magnitude of average velocity of the particle in 5 sec respectively are

A
3 m/s,175 m/s
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B
3 m/s,315 m/s
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C
175 m/s,3 m/s
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D
175 m/s,175 m/s
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Solution

The correct option is A 175 m/s,3 m/s
Given, v(t)=82t, we will check if the particle has changed its direction or not within the asked time interval, i.e. the time when velocity of the particle becomes zero.
82t=0 t=4 sec
Also, we know that
xfxi=t0v(t)dt=t0(82t)dt
xfxi=8tt2
Let particle starts from origin i.e xi=0
So, at t=0,xf=0,
at t=4,xf=8×442=16 m
at t=5,xf=8×552=15 m
The motion of the particle can be represented as shown

So, the average speed of the particle is 16+15=175 m/s
and, average velocity is 155=3 m/s

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