Question

If an object is moving at a constant velocity, is there no work done on that object?

Answer 1

Hint:As we know that, when the velocity is constant, that means an object is not changing its speed or its acceleration, and if the acceleration is not there, that means work is not done. Work done depends on the rate of change in velocity.

Complete step by step answer:
As per the question, if an object is moving at a constant velocity, then an acceleration of an object is zero or in this case the velocity does not change, so there can be no area under the acceleration graph:
$\mathop a\limits^ \to = 0$
where, $\mathop a\limits^ \to $ is the acceleration towards the direction of velocity of an object.
Now, we will find the force exerted by an object towards the direction of acceleration:
$\therefore \mathop F\limits^ \to = m.\mathop a\limits^ \to $
And, as we concluded above, acceleration is zero, we get:
$ \Rightarrow \mathop F\limits^ \to = 0$
So, the force exerted by an object is also zero due to the acceleration.
Now, to find the work done on that object:-
$\therefore W = F.S$
where, $W$ is the work done,
$F$ is the force exerted by an object, and
$S$ is the distance covered by an object.
And as we concluded above, the force exerted is zero.
So, the work done is also zero:
$ \Rightarrow W = 0.S = 0$
Hence, there is no work done on that object, if it is moving at a constant velocity.

Note:A horizontal line with a slope of 0 shows that the object is travelling at constant velocity and has no acceleration. If a line on a graph has a positive slope, the object is said to have positive acceleration; if the line has a negative slope, the item is said to have negative acceleration.