# 4. Calculating Acceleration

# Success Criteria

Your learning has been successful if you can do the following:

Define acceleration and its units.

Calculate acceleration from speed and time measurements.

Rearrange the equation 'a = Δv / Δt' to solve for 'v' and 't'

# Vocabulary

Learn these so you can communicate this concept well.

Acceleration: The rate at which an object's velocity changes over time. It can involve speeding up, slowing down, or changing direction.

Average acceleration: The change in velocity divided by the time taken for the change to occur. It represents the average rate at which an object's velocity changes.

Constant acceleration: When an object's velocity changes at a steady rate over time. This means the object is experiencing the same amount of acceleration throughout the entire motion.

Deceleration: The negative acceleration of an object, indicating a decrease in velocity over time. It's also known as negative acceleration or slowing down.

Velocity: How fast an object moving. It includes both the speed and direction of motion.

Do Now:

Collect and complete this small 'Do Now'. Then glue into your SciPAD page 11. Use your commonsense when glueing - don't glue straight on-top of words!

Find some space on page 15 of your PESS1.2 SciPAD,

and answer the following questions:

What does each letter in CUTLASS stand for?

## What is Acceleration and How is it Calculated?

As you learned in Lessons 2 and 3, the steeper the slope of a line on a distance-tiime graph, the faster the object is moving. An object that is ACCELERATING will give a graph line that is getting steeper - i.e. it is a curve.

In region A of the graph, the line is near horizontal - i.e. slow speed.

In region B of the graph, the line is near vertical - i.e. fast speed.

Therefore, the object is accelerating!

ACCELERATION is the measure of an increase in SPEED / VELOCITY in a certain TIME.

As you place your foot on the accelerator of a car, the velocity increases and the car accelerates. A large acceleration is a rapid change in velocity.

The size of the acceleration can be calculated by dividing the change in speed by the change in time.

DECELERATION is a decrease in speed in a certain time.

Note:

Change in speed, Δv = final speed - initial speed

If the acceleration is negative, we say it is 'deceleratiing'. Decelerating can be thought of as negative acceleration.

The SI unit for acceleration is metres per second per second, which can be written as or ms⁻²

If we know any two of these three measurements (i.e. acceleration, change in speed and change in time), we can calculate the third.

You may use the Triangle Method or the Cancelling Method from Lesson 1 to rearrange the equation.

## Constant Acceleration

If something is moving with CONSTANT ACCELERATION then its speed is changing by equal amounts in equal times.

For example, if a stationary cyclist starts pedalling and his speed increases by 3 ms⁻¹ every second then he will have a constant acceleration of 3 ms⁻².

This can be shown in the following table for the first 5 seconds of his ride.

In the next example, the speed is changing but not by equal amounts in equal times. Can you see that the increase in speed each seccond is now different?

You can, however, still calculate the AVERAGE ACCELERATION using the same formula as above:

average acceleration = Δv / Δt = (17-3) / (5-1) = 3.5 ms⁻²

Example 1

In order to catch a mouse, a crouching cat reaches a speed of 15 ms⁻¹ in 3 seconds. What is the cat's acceleration?

Example 2

The driver of a car travelling at 100 km/h (28 ms⁻¹) on the open road can see houses and a 50 km/h (14 ms⁻¹) road sign in the distance. If the driver takes 5 seconds to slow down to the 50 km/h speed limit, what is the car's average decceleration in ms⁻²?