# Speed, Velocity and Acceleration (A Level)

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## Speed

Speed is the rate of change of distance traveled with respect to time. It is a scalar quantity.

SI unit for speed: $\text{m s}^{-1}$

### Average speed:

$$\frac{\text{Total} \, \text{Distance}}{\text{Total} \, \text{Time}} \: = \: \frac{\Delta x}{\Delta t}$$

Note: The upper case symbol for the Greek letter delta, $\Delta$ is used to mean a change in a quantity.

### Instantaneous Speed:

$$\text{Rate of change of distance with respect to time at that instant} = \frac{dx}{dt}$$

## Velocity

Velocity is the rate of change of its displacement with respect to time. It is a vector quantity.

SI unit for velocity: $\text{m s}^{-1}$

Magnitude of velocity at a given point is given by instantaneous speed at that point.

Direction of velocity is tangential to path of object.

### Average Velocity:

$$\frac{\text{Total} \, \Delta \, \text{in} \, \text{Displacement}}{\text{Total} \, \text{Time}} \: = \: \frac{\Delta s}{\Delta t}$$

### Instantaneous Velocity:

$$\text{Rate of change of displacement with respect to time at that instant} = \frac{ds}{dt}$$

## Acceleration

Acceleration of an object is the rate of change of its velocity with respect to time. It is a vector quantity.

SI unit for acceleration: $m \, s^{-2}$

An object can be stated to be accelerating if ONE of the following criteria is fulfilled:

• $\Delta$ in magnitude only
• $\Delta$ in direction only
• $\Delta$ in both magnitude and direction

### Average Acceleration:

$$a \, = \, \frac{v – u}{t}$$

$$a \, = \, \frac{\Delta v}{\Delta t}$$

### Instantaneous Acceleration:

$$\frac{dv}{dt}$$