A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to
Step 1: Given data
A body is moving unidirectionally under the influence of a source of constant power.
Step 2: Formula used
Step 3: Calculating displacement
Now, the total work done by this force is equal to the product of the magnitude of applied force and the distance travelled by the body.
Substituting the value of work done in the power formula
Now as the velocity is given by and the force is given by
The power can be expressed as
Finally, we substitute to obtain
Now Newton’s first equation of motion gives the displacement of the body as
We assume that the body was initially at rest, i.e., .
So equation (ii) becomes
Substituting equation (i) and (iii) we get,
On simplifying we get,
Hence, its displacement is directly proportional to time .