Question

24. A particle moves in a straight line in such a way that its velocity v at any position x is given by v2 = 2-3x, where
x is measured from a fixed point. The acceleration of particle is
(1) Uniform
(2) Zero
(3) Non-uniform
(4) Indeterminate
​

Answer 1

Explanation:

Please find below the solution to the asked query:

Given above:

v2 = 2 - 3x ----- (1)

also we know that:

velocity = v = dx/dt

acceleration = a = dv/dt

and,

dividing and multiplying by dx on R.H.S.

dv/dt = dv/dx × dx/ dt ( and dx/dt = v)

a = dv/dt = v dv/dx ---- (2)

thus,

a = dv/dx × dx/ dt

differentiating (1) w.r.t. 'x'

2v dv/dx = d (2-3x) / dx

2v dv/dx = -3

v dv/dx = -3/2

comparing from equation (2) we have,

a = -3/2 correct answer....

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