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Question

When a particle's displacement x at the time t is given by x=At2+Bt+C, where A,B,andC are constants and v is the particle's velocity, the number 4Ax-v2is found


A

4AC+B2

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B

4ACB2

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C

2ACB2

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D

2AC+B2

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Solution

The correct option is B

4ACB2


Step: 1 GIven data:

Displacement of the particle x=At2+Bt+C.

Step: 2 Formula used:

Velocity = Change in position with respect to time = dxdt.

Step: 3 Calculate the value of 4Ax-v2 :

x=At2+Bt+C

dxdt=dAt2+Bt+Cdt=2At+B

Therefore, v=2At+B.

v2=2At+B2v2=4A2t2+4ABt+B2

Therefore,

4Ax=4A2t2+4ABt+4ACv24Ax=B24AC4AXv2=4ACB2

Hence option B is correct.


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