Acceleration

Key Stage 3

Meaning

Acceleration is an increase in speed.

Noun: Acceleration

Verb: To accelerate

About Acceleration

The opposite of acceleration is deceleration which is to slow down.

Acceleration happens when an object experiences Unbalanced Forces.

Acceleration Equation

\[a = {\tfrac{v-u}{t}} \] Where:

a = acceleration

v = final speed

u = initial speed

t = time

Example Calculations

A person starts at rest and accelerates to a speed of 8m/s in 0.8 seconds. Calculate the acceleration of the person.	A racing car travels comes around a corner at a speed of 20m/s and in 1.5 seconds accelerates to a speed of 80m/s. Calculate the acceleration of the racing car.
final speed = 8m/s initial speed = 0m/s time = 0.8s \(a = {\tfrac{v-u}{t}} \) \(a = {\tfrac{8-0}{0.8}} \) \(a = {\tfrac{8}{0.8}} \) \(a = 10m/s/s \)	final speed = 80m/s initial speed = 20m/s time = 1.5s \(a = {\tfrac{v-u}{t}} \) \(a = {\tfrac{80-20}{1.5}} \) \(a = {\tfrac{60}{1.5}} \) \(a = 40m/s/s \)
A horse begins trotting at 3.0m/s and accelerates to canter at 11m/s in 2.0 seconds. Calculate the acceleration of the horse.	A space probe is travelling at 18,000m/s and uses a thruster for 250 seconds to slow down to 6,000m/s. Calculate the acceleration of the space probe.
final speed = 11m/s initial speed = 3.0m/s time = 2.0s \(a = {\tfrac{v-u}{t}} \) \(a = {\tfrac{11-3.0}{2.0}} \) \(a = {\tfrac{8.0}{2.0}} \) \(a = 4m/s/s \)	final speed = 18,000m/s initial speed = 6,000m/s time = 250s \(a = {\tfrac{v-u}{t}} \) \(a = {\tfrac{18,000-6,000}{250}} \) \(a = {\tfrac{12,000}{250}} \) \(a = 48m/s/s \)

Key Stage 4

Meaning

Acceleration is a vector quantity that describes a change in velocity.

About Acceleration

Acceleration is a vector because it has a magnitude and direction.

The SI Units of acceleration and metres per second per second (m/s/s).

Acceleration may refer to:

• Increasing speed - The magnitude of the velocity increases.
• Decreasing speed - The magnitude of the velocity decreases, also known as deceleration.
• Changing direction - The magnitude of the velocity remains constant (constant speed) but the object changes direction of travel.

Acceleration occurs due to unbalanced forces on an object.

Examples

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This animation shows a linear acceleration as the objects roll down the slope.	This animation shows acceleration due to a changing direction.

Equation

Acceleration, Velocity and time

NB: You must remember this equation.

This equation applies to linear acceleration but not to a change in direction.

\(a = {\tfrac{\delta v}{t}} \)

Where\[a\] = Acceleration of the object.

\(\delta v\) = Change in magnitude of the velocity.

\(t\)= Time taken for the change in velocity.

Example Calculations

A person starts at rest and accelerates to a speed of 8m/s in 0.8 seconds. Calculate the acceleration of the person.	A racing car travels comes around a corner at a speed of 20m/s and in 1.5 seconds accelerates to a speed of 80m/s. Calculate the acceleration of the racing car.
final speed = 8m/s initial speed = 0m/s time = 0.8s \(a = {\tfrac{v-u}{t}} \) \(a = {\tfrac{8-0}{0.8}} \) \(a = {\tfrac{8}{0.8}} \) \(a = 10m/s/s \)	final speed = 80m/s initial speed = 20m/s time = 1.5s \(a = {\tfrac{v-u}{t}} \) \(a = {\tfrac{80-20}{1.5}} \) \(a = {\tfrac{60}{1.5}} \) \(a = 40m/s/s \)
A horse begins trotting at 3.0m/s and accelerates to canter at 11m/s in 2.0 seconds. Calculate the acceleration of the horse.	A space probe is travelling at 18,000m/s and uses a thruster for 250 seconds to slow down to 6,000m/s. Calculate the acceleration of the space probe.
final speed = 11m/s initial speed = 3.0m/s time = 2.0s \(a = {\tfrac{v-u}{t}} \) \(a = {\tfrac{11-3.0}{2.0}} \) \(a = {\tfrac{8.0}{2.0}} \) \(a = 4m/s/s \)	final speed = 18,000m/s initial speed = 6,000m/s time = 250s \(a = {\tfrac{v-u}{t}} \) \(a = {\tfrac{18,000-6,000}{250}} \) \(a = {\tfrac{12,000}{250}} \) \(a = 48m/s/s \)