CIE A-Level Physics: Equations of Motion

Vocabulary terms covering kinematics including displacement, velocity, acceleration, graph interpretations, SUVAT equations, and projectile motion based on the Cambridge (CIE) A-Level Physics syllabus.

Distance

A measure of how far an object travels; it is a scalar quantity with magnitude only.

Displacement

A measure of how far something is from its starting position, along with its direction. It is a vector quantity defined as the change in position.

Speed

A scalar quantity reflecting the distance an object travels every second. Average speed is calculated as $\text{total distance} / \text{time taken}$. Units are $\text{m s}^{-1}$.

Velocity

A vector quantity defined as the rate of change of displacement. It describes both magnitude and direction.

Acceleration

Defined as the rate of change of velocity, measured in $\text{m s}^{-2}$. It describes how much an object's velocity changes every second.

Gradient of a Displacement-Time Graph

This value represents the velocity of the object. A positive gradient indicates constant velocity in the positive direction.

Area under a Velocity-Time Graph

This value is equal to the displacement of a moving object.

Gradient of a Velocity-Time Graph

This value is equal to the acceleration of the object.

Area under an Acceleration-Time Graph

This value represents the change in velocity.

Area under a Speed-Time Graph

This value equals the distance travelled.

Kinematic Equation for Final Velocity (v)

$v = u + at$ where $u$ is initial velocity, $a$ is acceleration, and $t$ is time.

Kinematic Equation for Displacement (s) involving average velocity

$$s = \frac{1}{2}(u + v)t$$

Kinematic Equation for Displacement (s) involving time and acceleration

$$s = ut + \frac{1}{2}at^2$$

Kinematic Equation for Final Velocity Squared ($v^2$)

$$v^2 = u^2 + 2as$$

Acceleration of Free Fall (g)

In vertical motion on Earth, this value is taken as $9.81\text{ m s}^{-2}$.

Projectile Motion components

The vertical and horizontal components of the motion are completely independent of one another and must be evaluated separately.

Time of flight

The total duration a projectile remains in the air.

Maximum height attained

The vertical height at which the projectile is momentarily at rest ($v = 0$).

Range

The total horizontal distance travelled by a projectile.