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Question

The motion of a particle along a straight line is described by the function x=6+4t2t4 where x is in meters and t is in seconds. What is the maximum velocity attained by the particle ?

A
16323 m/s
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B
14323 m/s
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C
14332 m/s
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D
16332 m/s
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Solution

The correct option is A 16323 m/s
We know that velocity is rate of change of position with respect to time, function of position is given as x=6+4t2t4

Velocity, v=dxdt=8t4t3
acceleration a=dvdt=812t2
For finding the maxima of any function we diffrentiate it and equate to zero.

Velocity is maximum when dvdt=0
812t2=0t=23

Now by substituting the time in the function of velocity we get,
maximum velocity,
=8234.23.23
=16323 m/s

Hence option A is the correct answer

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