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Question

Velocity of a particle moving along x-axis is given as v=t24t

A
Particle accelerates for 0t<2
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B
Particle accelerates for 2t4
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C
Maximum speed attained by the body between 0 to 4 sec is 4 m/s
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D
Particle retards for 2<t4
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Solution

The correct options are
C Maximum speed attained by the body between 0 to 4 sec is 4 m/s
D Particle retards for 2<t4
a=dvdt=2t4
a<0 from 0 s to 2 s, therefore it is retarding
a>0 from 2 s to 4 s therefore it is accelerating
As it is retarding for the first 2 seconds, the minimum velocity occurs at t = 2 sec and it is equal to v(2)=224×2=4m/s. Miniumum negative velocity means maximum speed.
maximum speed is 4 m/s

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