Acceleration

Acceleration

When we discussed velocity and speed, we assumed a constant velocity. However, this is rarely the case in the real world. In the real world the velocity of an object in motion is often changing. 

What is acceleration? 

Acceleration is the measurement of change in an object's velocity. When you press down on the gas pedal in a car, the car surges forward going faster and faster. This change in velocity is acceleration. 

The equation for calculating acceleration is: 

Acceleration = (change in velocity)/(change in time) 
or 
a = Δv ÷ Δt

How to Measure Acceleration 

The standard unit of measurement for acceleration is meters per second squared or m/s². You can calculate this from the above formula where velocity is meters per second and time is in seconds. 

Acceleration is a Vector 

In physics acceleration not only has a magnitude (which is the m/s² number we discussed above), but also has a direction. This makes acceleration a vector. 

Force and Acceleration 

Newton's second law of motion states that the force on an object equals the mass times the acceleration. This is written in the following equation: 

Force = mass * acceleration 
or 
F = ma

We can use this formula to also figure out the acceleration if we know the mass and force on an object. This formula is: 

acceleration = force/mass 
or 
a = F/m

Constant Acceleration 

When an object is changing velocity by a constant amount over time, this is called constant acceleration. An object with constant positive acceleration will be going faster and faster. Its velocity will be increasing constantly. 

Interval 1st second 2nd second 3rd second

Acceleration 5 m/s2 5 m/s2 5 m/s2

Velocity 10 m/s 15 m/s 20 m/s

An example of constant acceleration of 5 m/s².

Free Fall: A Type of Acceleration 

One example of constant acceleration is an object in free fall. During free fall, gravity applies a constant force on the object causing a constant increase in velocity. If you were to measure the distance an object fell, each second it would fall further because it is constantly picking up speed. 

Note: In the real world there would be the additional force of air friction on the object. At some point the object would reach "terminal velocity". This means that it would no longer accelerate and the speed of the fall would stay the same. The terminal velocity of a skydiver falling face down is around 122 miles per hour. 

Average Acceleration 

The average acceleration is the total change in velocity divided by the total time. This can be found using the equation a = Δv ÷ Δt. 

For example, if the velocity of an object changes from 20 m/s to 50 m/s over the course of 5 seconds the average acceleration would be: 

a = (50 m/s - 20 m/s) ÷ 5s 
a = 30 m/s ÷ 5s 
a = 6 m/s² 

Deceleration or Negative Acceleration 

When the velocity of an object decreases (slows down) this is called deceleration. It may also be represented by a negative acceleration. This means the direction or vector of the acceleration is pointing in the opposite direction of the movement of the object. 

For example, if the velocity of an object changes from 40 m/s to 10 m/s over a time interval of 2 seconds the average acceleration would be: 

a = (10 m/s - 40 m/s) ÷ 2s 
a = -30 ms ÷ 2s 
a = -15 m/s² 
This could also be called a deceleration of 15 m/s².