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Question

If velocity of a particle is v(t)=t23t m/s, the average speed and magnitude of average velocity of the particle in 6 sec respectively are

A
6 m/s,3 m/s
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B
4.5 m/s,4.5 m/s
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C
4.5 m/s,3 m/s
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D
3 m/s,3 m/s
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Solution

The correct option is C 4.5 m/s,3 m/s
Given, v(t)=t23t, 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.
t23t=0 t=0,3 sec
Also, we know that
xfxi=t0v(t)dt=t0(t23t)dt
xfxi=t333t22
Let particle starts from origin i.e xi=0
So, at t=0,xf=0,
at t=3,xf=3333×322=92 m
at t=6,xf=6333×622=18 m

So, the average speed of the particle is |92|+|92|+186=276=92=4.5 m/s
and, average velocity is 186=3 m/s

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