Question

If the velocity position (v-x) relation of a particle moving in a straight line is given as v2 = a – bx2 (where a and b are constants) then the acceleration of the particle is proportional to

Answer 1

Answer:

acceleration is proportional to distance x

i.e. a ∝ x

Explanation:

As given velocity

$v^{2} =a-bx^{2}$

differentiating both sides w.r.t. x

$2v\frac{dv}{dx} =-2bx$

or, $v\frac{dv}{dx} =-bx$

But we know that acceleration a is rate of change of velocity

$a=\frac{dv}{dt}$

or, $a=(\frac{dv}{dt}/\frac{dx}{dt} )\frac{dx}{dt}$

or, $a=v\frac{dv}{dx}$

or, $a=-bx$

Thus, a ∝ x