# Acceleration: Definition, Equation and Examples

## Cheetah Drag Racing

I'm sorry if you've heard this one before, but the cheetah is the king of fast. At its best, a cheetah can run over 100 km/hr. By itself, this is an incredible feat. But what I find even more incredible is that the cheetah is able to be standing still one second and three seconds later it's running 100 km/hr! Most of your high-end cars require between four and six seconds to do what that cheetah does in three seconds. And with this quick analogy, we can get to the meat of this lesson: acceleration.

## Acceleration

**Acceleration** is the rate of change of an object's velocity. Remember, velocity is how fast an object is moving in a specific direction. So, acceleration measures how fast the velocity changes. We can calculate acceleration if we know the total change in velocity and the time it takes for the velocity to change. The equations are:

Average acceleration = change in velocity / change in time

Change in velocity = final velocity - starting velocity

The units for acceleration are m/s^2, but something else is required. Acceleration, like velocity, is a vector quantity. This means that you need to specify the direction of motion as well. This could be a compass point, like north and east, or a simple description like right or left or up or down, depending on the question. In addition, acceleration can be positive or negative. If a car, for example, is traveling in a straight line and its speed increases, the acceleration is positive. If that car slows down, its acceleration is negative.

I want to pause for a minute here to clarify a couple of points. First, in everyday usage, acceleration has come to mean speeding up. If you press on the accelerator in your car, the car's speed increases. Acceleration has a slightly different meaning in physics, though. The definition specifically mentions a change in velocity, not speed.

Remember, velocity has a direction attached, so if the direction of travel changes, the velocity changes, even if the speed remains constant. Picture setting the cruise control on the car at 40 km/hr and driving in a circle. Speed is a constant 40 km/hr, but velocity changes every time you change direction. Since velocity is changing, you can calculate acceleration even though the speed is constant. Acceleration is not dependent on a change in speed.

The second point involves the term deceleration, commonly used to mean slowing down. The term deceleration is not commonly used in physics. Instead, deceleration is more often called negative acceleration.

## Solving Acceleration Problems

Remember the cheetah from the introduction? Let's use what we just learned about acceleration to calculate the acceleration of the cheetah. We know that the cheetah has an initial velocity of 0 km/hr because he's standing still, stalking his prey. When he's ready to attack, he can reach a speed of 100 km/hr in 3 seconds. First, we need to convert kilometers per hour to meters per second.

100 km x 1000 m/km = 100,000 m

1 hour x 60 min/hr x 60 sec/min = 3600 seconds

100,000 m / 3600 sec = 27.8 m/s

The cheetah starts with a velocity of 0 m/s because he is not moving. He begins running west, after a gazelle, and reaches a maximum velocity of 27.8 m/s west in 3 sec.

Average acceleration = change in velocity / change in time

Average acceleration = (27.8 m/s west - 0 m/s) / 3 sec = (27.8 m/s west) / 3 sec = 9.3 m/s^2 west

This means that for every second the cheetah is running, his velocity increases by 9.3 m/s. Since he is increasing his speed in a constant direction (west), this is positive acceleration. The directional term west is required because acceleration is a vector.

Let's look at another example. A driver traveling north at 90 km/hr in a zone with a speed limit of 40 km/hr sees a police officer. The drivers slows to 35 km/hr to avoid getting a speeding ticket. It takes 8 seconds to slow the car down to 35 km/hr. What is the acceleration?

90 km/hr = 25 m/s

35 km/hr = 9.7 m/s

Average acceleration = change in velocity / change in time

Average acceleration = (9.7 m/s north - 25 m/s north) / 8 seconds = -15.3 m/s north / 8 sec = -1.9 m/s^2 north

In this case, the car is slowing down so the acceleration is negative.

## Lesson Summary

**Acceleration** is the rate of change of an object's velocity. Acceleration is a vector quantity, requiring both a magnitude and a direction. In addition, acceleration can be positive (if the object's velocity increases) or negative (if the object's velocity decreases). Remember, acceleration is not dependent on a change in speed. Velocity changes if the direction of travel or speed changes. Even if the object is moving at a constant speed, the object can be accelerating if the direction of travel changes. The equation to solve acceleration problems is: average acceleration = change in velocity / change in time.

## Learning Outcomes

Through this video lesson, you can prepare to:

- Describe what acceleration means in physics
- Discern the difference between acceleration as it relates to physics and the 'everyday' meaning of acceleration
- Rewrite the formula for finding average acceleration
- Differentiate between positive and negative acceleration

To unlock this lesson you must be a Study.com Member.

Create your account

### Register to view this lesson

### Unlock Your Education

#### See for yourself why 30 million people use Study.com

##### Become a Study.com member and start learning now.

Become a MemberAlready a member? Log In

Back### Resources created by teachers for teachers

I would definitely recommend Study.com to my colleagues. It’s like

**a teacher waved a magic wand and did the work for me.** I feel like it’s a lifeline.