Question

What is the acceleration of a body moving with uniform velocity?

Answer 1

Hint: In order to solve this question we need to understand that velocity is defined as displacement by a body per unit time interval while the acceleration is defined as velocity of body per unit time interval, however this is case when the distance is numerically defined but when the distance travelled by body is function of “x” then velocity is defined as derivative of distance with respect to time and acceleration is defined as derivative of velocity with respect to time.

Complete step by step answer:
Let the distance travelled by body denoted by $x$.Since the distance is variable so velocity is defined as,
$v = \dfrac{{dx}}{{dt}}$
And similarly acceleration is defined as,
$a = \dfrac{{dv}}{{dt}}$
Since the velocity is uniform, so velocity is constant,
$v = k$
where $k$ is constant.
So, acceleration is defined as,
$a = \dfrac{{dk}}{{dt}}$
$\therefore a = 0\,m{\sec ^{ - 2}}$
The derivative of a constant term is always $0$. So the acceleration of the body would be zero.

Hence, the acceleration of a body moving with uniform velocity will always be zero.

Note: It should be remembered that acceleration is that fundamental physical quantity which is the result of force acting on a body and thus this acceleration is the cause of motion in all objects in the universe either acceleration can be constant or increasing or decreasing with respect to time. Also velocity is defined graphically as slope of distance time graph, and distance is defined graphically as area under velocity time graph. Similarly velocity can also be defined from acceleration time graph as the area under acceleration time graph, and acceleration can be defined as slope of velocity time graph.