# Is the acceleration of an object at rest zero?

This is part of a series on common misconceptions.

Is this true or false?

When the object is at rest, then its acceleration has to be zero.

**Why some people say it's true:** Acceleration is speed divided by time.

**Why some people say it's false:** Acceleration is the rate of change of velocity.

The statement is \( \color{red}{\textbf{false}}\).

Explanation:Generally, it is thought that the acceleration is simply the ratio of speed and time. But, this is false. Acceleration is defined as the rate of change of velocity. It may happen that at a certain instant of time the speed is zero, but the very next instant it changes and becomes non-zero. In a very little time difference, there may be a very tiny change in speed.

Now, for the acceleration, it does not matter how large or small is the speed, but rather what matters is how fast it is changing. If the rate of change is high then the acceleration is also large.

To delve deeper, let's take some examples. A car starts from rest, then at first accelerator is needed to be pressed. The accelerator gives acceleration to the car and starts increasing its speed. Therefore, at the start of motion of the car, its speed was zero but the acceleration was non-zero.

Rebuttal: What does the ratio of speed and time give.

Reply: No physical quantity is yet defined which is denoted by the ratio of speed and time. This ratio equals the average acceleration under some conditions, which are

- At the start of motion, the object is at rest

- The object moves on a straight path

Rebuttal: Is it necessary to take small time interval for acceleration?

Reply: Yes, the acceleration can be categorized into two types.

- Instantaneous acceleration

- Average acceleration

In the case of instantaneous acceleration, change in velocity has to be taken in a small differential time interval. The instantaneous acceleration is defined as \[\vec a = \frac{{d\vec v}}{{dt}}\]

If a particle is thrown vertically upwards then it stops momentarily at the highest point of motion. What is the acceleration of the particle at the highest point motion?

Assume size of the particle to be negligible.

**See Also**

**Cite as:**Is the acceleration of an object at rest zero?.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/is-the-acceleration-of-an-object-at-rest-zero/