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