
How do we describe speeding up or slowing down? What is the difference between slowing down gradually and hitting a brick wall? Both these questions have answers that involve acceleration. Acceleration describes how velocity changes. Any change in velocity, including speeding up, slowing down, or turning, creates acceleration.

What is acceleration?

Almost nothing moves at constant speed for very long in everyday life. Even a car on cruise control speeds up and slows down by small amounts to compensate for hills. How do we describe changes in velocity, such as going from rest to moving, or from moving to rest? The answer is the concept of acceleration. Acceleration is defined in equation (4.1) as the rate of change of velocity.

(4.1)  $$a=\frac{\text{\Delta}v}{\text{\Delta}t}$$
 a  =  acceleration (m/s^{2})  Δv  =  change in velocity (m/s)  Δt  =  change in time (s) 
 Acceleration definition 

Acceleration is a crucial concept in the physics of motion because acceleration, not velocity, is the result of applied forces.

Equation (4.1) describes how acceleration is the change in velocity (Δv = v_{f} − v_{i}) divided by the change in time (Δt = t_{f} − t_{i}).
For example, if a car starts at rest and is moving at 30 mph, then 10 s later the car’s acceleration is 3 mph/s, or three miles per hour per second.
The speedometer increases by 3 mph each second for 10 s. Acceleration is the rate at which velocity changes.

A car provides a good reference for developing an intuitive feel for acceleration. Suppose your speed goes from 0 to 29 m/s in 10 s. This is a typical acceleration for a small to midsize car. The change in speed is 29 m/s (29 m/s − 0 m/s). The change of 29 m/s divided by 10 s gives an acceleration of 2.9 m/s per second. The acceleration is 2.9 meters per second per second because your car accelerated, or gained 2.9 m/s of speed each second for 10 s.

The units of acceleration are units of velocity divided by units of time. For a typical car a convenient unit would be miles per hour per second. A powerful sports car can accelerate from zero to 60 mph in 4 s. The change in velocity is 60 mph. The change in time is 4 s. The acceleration is 15 mph per second.

Acceleration in this course will usually be expressed in SI units of m/s per second, or m/s^{2}. (This is sometimes written as m/s/s or m s^{−2}.) One meter per second squared means that the velocity changes by one meter per second each second.


Acceleration can be positive or negative. For example, an acceleration of +4 m/s^{2} adds 4 m/s of velocity each second. A car starting from rest would move at 4 m/s after one second, 8 m/s after two seconds, 12 m/s after three seconds, and so on. A negative acceleration of −4 m/s^{2} subtracts 4 m/s every second. A car moving at +40 m/s would be moving at 36 m/s after one second, 32 m/s after two seconds, 28 m/s after three seconds, and so on.
A negative acceleration is sometimes called a deceleration.

When an object moving with positive velocity is slowing down, the acceleration that it experiences is ___________.
 positive
 negative
 zero
 infinite

The correct answer is b, “negative.”

A man is driving his car north on the highway at a constant velocity of 50 mph for 100 s. What is the value of his acceleration?
 0.5 m/hr/s
 5,000 m/hr/s
 0 m/hr/s
 not enough information

The correct answer is c, 0 m/hr/s or 0 m/(hr s).
Constant velocity indicates zero acceleration.
