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Question

The position of a particle is given by ¯¯¯r=3t2^ı+3t^ȷ+4^k where t is in second and the coefficient have proper units for ¯¯¯r to be in meter. The acceleration of the particle at t=2s is

A
4ms2 along ydirection
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B
3ms2 along xdirection
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C
4ms2 along xdirection
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D
2ms2 along zdirection
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Solution

The correct option is A 4ms2 along ydirection
Given,
¯¯¯r=2t2ˆi+2tˆj+4ˆk
Now,
Velocity will be
V=drdt=3ˆi+8ˆjAtt=2sv=3ˆi+8ˆjm/s
Similarly the acceleration is
a=dvdt=0+4ˆj
Therefore, the acceleration is independent of t and is a constant 4ˆjm/s2.

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