# Is acceleration the rate of change of speed?

This is part of a series on common misconceptions.

Is this true or false?

Acceleration is the rate of change of speed.

**Why some people say it's true:** Think of accelerating in a car: when you hit the gas, you speed up, and when you hit the brake, you slow down. Acceleration is generally associated with a change in speed.

**Why some people say it's false:** In physics, direction matters. If the direction of motion changes, this could be considered acceleration too, even if the speed stays constant.

The statement is $\color{red}{\textbf{false}}$.

Explanation:Acceleration is defined as the rate of change of velocity. Velocity is a

vector, which means it contains a magnitude (a numerical value) and a direction. So the velocity can be changed either by changing the speed or by changing the direction of motion (or both). Therefore, it may be possible that the speed is constant, but the velocity is changing because the direction is changing. In this case, acceleration will be non-zero and equal to the rate of change of velocity.It is a general misconception that rate of change of speed is equal to the magnitude of the rate of change of velocity. However, this is not true in all cases. Consider uniform circular motion: in the case of a uniform circular motion, the particle moves on a circular path with uniform speed. The speed remains constant, but the direction of motion is continuously changing. Due to change in direction of motion, acceleration is non-zero. This acceleration is toward the center of the circle and known as centripetal acceleration.

In general, acceleration can be resolved into two components. One component, which is parallel to the velocity, is known as tangential acceleration. This component changes the speed of the particle and is equal to the rate of change of speed. The other component of acceleration, which is perpendicular to velocity, is known as normal acceleration. This component is responsible for changing the direction of the velocity.

Velocity is the rate of change of displacement, while speed is the rate of change of distance. In other words, velocity is the rate of change of the shortest distance moved by a body from the final position to the initial position, while speed is the rate of change of the total length of the path traveled by a certain body.

Query: What can be said about the acceleration of a particle moving in a zig-zag path with constant speed?

Reply: The acceleration of the particle has to be non-zero, as the particle is changing its direction. However, the tangential component of the acceleration is zero, as the speed remains constant.

Query: If both the speed and direction changes, then is it possible to have zero acceleration?

Reply: No. If speed changes, then tangential acceleration is non-zero. If the direction of motion is changing, then normal acceleration is non-zero. The result of these two accelerations can never be zero as they are perpendicular to each other.

A particle is moving on a circular track with constant non-zero speed. Which of the following options are correct?

(a) The acceleration of the particle is zero.

(b) The rate of change of speed equals the magnitude of the rate of change of velocity.

(c) Instantaneous speed equals the magnitude of instantaneous velocity.

(d) The angle between velocity and acceleration has to be $90^\circ$.

**See Also**

**Cite as:**Is acceleration the rate of change of speed?.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/is-acceleration-the-rate-of-change-of-speed/