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Question

A particle moves in a straight line so that its velocity at any point is given v2=a+bx, where a, b≠0 are constants. The acceleration is


A

Zero

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B

Uniform

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C

Non-uniform

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D

Intermediate

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Solution

The correct option is B

Uniform


Step 1: Given data.

The velocity at any point, v2=a+bx

Where a and b are constant and x is the distance covered.

Step 2: Finding the acceleration of the particle.

We know that,

a=dvdt

Where a is acceleration and dvdtis change in velocity with respect to time.

Also,

v=dxdt

Now,

v2=a+bx Given

Differentiate the above equation both sides with respect to time.

dv2dt=da+bxdt

2vdvdt=bdxdt

2va=bv ∵Fromequationiandii

a=b2

Since, it is clear that the value of acceleration a is constant.

Therefore, acceleration is uniform.

Hence, option B is correct.


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