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Question

A particle moves along a straight line and its velocity depends on time as v=4tt2.Then for first 5 sec

A
average speed is 135 m/s
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B
average speed is 53 m/s
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C
average speed is 3215 m/s
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D
average speed is 35 m/s
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Solution

The correct option is A average speed is 135 m/s
Given, v(t)=4tt2, 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.
4tt2=0 t=0,4 sec
Also, we know that
xfxi=t0v(t)dt=t0(4tt2)dt
xfxi=2t2t33
Let particle starts from origin i.e xi=0
So, at t=0,xf=0,
at t=4,xf=2×42433=96643=323 m
at t=5,xf=2×52533=1501253=253 m
Hence, average speed is 323+(323253)5=135 m/s

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