Question

A particle starts from rest and is acted on by a net force that does work at a rate that is proportional to the time t. The speed of the particle is proportional to:_____

a. √t
b. t
c. t^2
d.1/√t
e. 1/t

Answer 1

Answer:

The speed of the particle is proportional to:

c. t²

Explanation:

Given;

initial velocity of the particle, u = 0

let the net force on the object = F

Work done on the particle is given by;

W = F x d

W ∝ t

$Fd \ \alpha \ t\\\\\frac{mv}{t}d \ \ \alpha \ t\\\\mvd \ \ \alpha \ t^2\\\\v \ \ \alpha \ t^2$

Therefore, the speed of the particle is proportional to t²

Answer 2

The speed of the particle is proportional to t.

It should be noted that work is a change in kinetic energy. Therefore, power will be calculated as:

Power = Work / Time = force × velocity

Power is proportional to t. Since force is a constant, then the velocity will be proportional to t. Therefore, the speed of the particle is proportional to t.

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