Question

What is the acceleration of an object if its velocity is constant?

Answer 1

Hint: To solve this question we need to have the concept of velocity and acceleration. Acceleration is defined as the rate of change of velocity. Mathematically the formula of acceleration is written as
\[\text{acceleration}=\dfrac{\vartriangle \text{velocity}}{\vartriangle \text{time}}\], which is the ratio of change in velocity to change in time. The question will be solved with the help of instance.

Complete step by step answer:
The question asks us to find the value of acceleration when velocity does not change with time which means the velocity is constant. Acceleration is defined as the rate of change of velocity. It could be written as the ratio of change in velocity to change in time. In mathematical form it is written as:
\[\text{acceleration}=\dfrac{\vartriangle \text{velocity}}{\vartriangle \text{time}}\]
Delta ($\vartriangle $) refers to the change in the value.
Since in the question it is given that velocity is a constant which means the velocity does not change with time, which means if at time ${{t}_{1}}$ the velocity given is ${{v}_{1}}$ then at ${{t}_{2}}$ also the velocity will be the same which is ${{v}_{1}}$ for an object under consideration. So on putting the values in the formula of acceleration we get:
\[\text{acceleration}=\dfrac{\vartriangle \text{v}}{\vartriangle \text{t}}\]
\[\Rightarrow \text{acceleration}=\dfrac{{{v}_{1}}-{{v}_{1}}}{{{t}_{2}}-{{t}_{1}}}\]
\[\Rightarrow \text{acceleration}=\dfrac{0}{{{t}_{2}}-{{t}_{1}}}\]
We know that when $0$ is divided by any number the value comes as $0$ itself.
\[\Rightarrow \text{acceleration}=0\]
$\therefore $ The acceleration of an object is zero if its velocity is constant.

Note: The minute value changes the velocity the acceleration will be written as\[\text{acceleration}=\dfrac{dv}{dt}\]. In the same manner the value of velocity is $0$ when the displacement is constant. So velocity is written as the ratio of change in displacement to change in time.