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

## If there is a constant velocity, then, ∆E = 0, which implies that $W = 0$. Am I wrong?

Aug 2, 2017

No work is done as acceleration is zero

#### Explanation:

If an object moves with constant velocity,
$\vec{a}$ = $\vec{0}$

$\vec{F} = m \cdot \vec{a}$

$\Rightarrow \vec{F} = \vec{0}$

$W = F \cdot S$

$\therefore W = 0$

Aug 2, 2017

The total work done on the object is indeed $0$.

#### Explanation:

If an object is moving with a constant velocity, then by definition it has zero acceleration.

And according to Newton's second law,

$\sum F = m a$

$\sum F = m \left(0\right) = 0$

So there is no net force acting on the object.

The simple equation for total work is

W_"tot" = sumF·s

Since the net force $\sum F$ is $0$,

W_"tot" = 0·s = color(blue)(ulbar(|stackrel(" ")(" "0" ")|)

The total work done on the object is thus color(blue)(0 (that's not to say that there isn't work done by individual forces on the object, but the sum is $0$).