Question

a particle moves a distance x in time t according to equation x= (t+5)^-1. The acceleration of particke is proprotional to?
(a) velocity^3/2. (b) distance ^2
(c) distance ^-2. (d) velocity ^2/3

Answer 1

The distance of the particle at time $t$ is

$x=(t+5)^{-1}$. The speed is given by

$v=\frac{dx}{dt}\\ v=\frac{d(t+5)^{-1} }{dt}\\ v=-(t+5)^{-2}$

The acceleration of the particle is

$a=\frac{dv}{t}\\ a=\frac{d(-(t+5)^{-2} )}{t}\\ a=2(t+5)^{-3} \\ a=2(-v)^{3/2}$

The acceleration is proportional to $velocity ^{3/2}$.

Correct choice is (a).

Answer 2

Answer:

Explanation:

Here's the solution to your question.

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