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Question

A particle is moving along x – axis whose position is given by x=4−9t+t33 . Mark the correct statement(s) in relation to its motion.

A
Direction of motion is not changing at any of the instants
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B
Direction of motion is changing at t=3 s
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C
For 0<t<3 s, the particle is slowing down
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D
For 0<t<3 s the particle is speeding up
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Solution

The correct options are
B Direction of motion is changing at t=3 s
C For 0<t<3 s, the particle is slowing down
x=49t+t33
Differentiating w.r.t t, we get
v=09+t2
v=t29
Putting v=0, we get
t=3 s
Direction of motion is changing at t=3 s
Differentiating v w.r.t t, we get
a=2t
We know that, if v and a are in opposite direction then the particle slows down.
For 0<t<3 s, v is in negative direction whereas a is positive , so the particle is slowing down.

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