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Question

The equation of motion of a particle moving along a straight line is s=2t39t2+12t, where the units of sand t are cm and sec. The acceleration of the particle will be zero after


A

32sec

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B

23sec

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C

12sec

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D

Never

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Solution

The correct option is A

32sec


Step 1: Given data:

Equation of motion, s=2t39t2+12t······1

Step 2: Formula used:

The relationship between acceleration and displacement is-

a=d2sdt2

Step 3: Calculation of time:

According to the formula, obtain the second derivative of equation 1 to get the acceleration,

The first derivative of equation 1 is,

dsdt=d2t3-9t2+12tdtdsdt=6t2-18t+12.......(2)

Again differentiate equation (2) with respect to time to obtain acceleration-

d2sdt2=12t-18a=12t-18

According to the problem, the particle's acceleration would be zero. So,

12t-18=012t=18t=32

Thus, the acceleration of the particle will be zero after 32sec.

Hence, option A is the correct answer.


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