The movement of objects can be described using motion graphs and numerical values. These are both used to help in the design of faster and more efficient vehicles.

This equation applies to objects in uniform acceleration:

- (final velocity)² = (initial velocity)² + (2 × acceleration × distance)

This is when:

- final velocity (v) is measured in metres per second (m/s)
- initial velocity (u) is measured in metres per second (m/s)
- acceleration (a) is measured in metres per second squared (m/s²)
- displacement (x) is measured in metres (m)

The equation above can be used to calculate the final velocity of an object if its initial velocity, acceleration and displacement are known. To do this, simplify the equation to find v:

A biscuit is dropped 300 m, from rest, from the Eiffel tower. Calculate its final velocity, ignoring air resistance. (Acceleration due to gravity = 10 m/s².)

The equation can also be used to calculate the acceleration of an object if its initial and final velocities, and the displacement are known. To do this, rearrange the equation to find a:

A train accelerates uniformly from rest to 24 m/s on a straight part of the track. It travels 1.44 km. Calculate its acceleration.

The equation can also be rearranged to find initial velocity (u) and displacement (x):

These equations of motion:

can be rearranged to form other useful equations to help work out.

becomes

or

can be written:

and rearranged as:

- Question
A toy rocket is fired vertically upwards against gravity with an initial velocity of 20 m/s. What height will it reach in 1 second if a = -10 m/s²? Ignore air resistance in your calculation.