Review of the unit so far...

• Frame of reference

• Measuring distance and direction with vectors

• Speed is how fast something is moving

• Velocity is speed and direction which can be measured with vectors

Acceleration is a change in velocity of an object.


Remember that velocity is the SPEED and DIRECTION of a moving object.

So, acceleration is a change in speed and/or direction.

Most people think of acceleration as speeding up. Like a car speeding up as it travels along a highway. BUT this is only one way an object can experience acceleration.

So acceleration is not just about speeding up!

• When an object slows down or changes direction, it involves acceleration.

• Even if speed remains constant, a change in direction results in acceleration.

Hitting a ball with a bat results in a change in the ball's direction and speed, resulting in acceleration.

Acceleration occurs when a racer crosses the finish line and begins to slow down.

A skydiver experiences different accelerations as they speed up during the fall and then slow down after opening their parachute.

​Calculating Acceleration

We will only be calculating acceleration when there is a change in speed (not direction).

To find acceleration without a change in direction, you divide the change in velocity by the change in time.

In this formula,

Remember that in acceleration the velocity is changing so we have to have two velocities in the formula.

Let's look at example #1:

A bicyclist is mountain biking down a hill.

They begin with a velocity of 1 meter/second. (initial velocity)
When they reach the bottom of the hill, they have a velocity of 6 meters/second. (final velocity)
It took them 5 seconds to reach the bottom of the hill.

Always begin by rewriting the information like this:

V₁ = 1 m/s
V₂ = 6 m/s
t = 5 seconds

Rewrite the equation for acceleration, then plug in the numbers and chug out the answer

If you leave out the units during the calculation, just be sure to have the final units of m/s²

​Example #2:

A skateboarder speeds up from a velocity of 2 m/s to a velocity of 8 m/s.
It took 3 seconds for this change to occur.

What was the acceleration?

Given:

v₁ = 2 m/s
v₂ = 8 m/s
t = 3 seconds

Plug and Chug

Velocity-Time Graphs
(shows the relationship between velocity and time)

Important: When reading a graph, study the x-axis and y-axis to understand what you are looking at.

1. Increasing velocity (positive acceleration) from 0 m/s to 8 m/s in 4 seconds

2. Constant velocity (zero/no acceleration) velocity stays the same at 8 m/s for 3 seconds

3. Decreasing velocity (negative acceleration/deceleration) 8/ms to 0 m/s in 3 seconds

​What did we learn today:

Acceleration measures the change in velocity of a moving object

​We can use a velocity-time graph to illustrate/model acceleration.