# Speed, Velocity and Acceleration (A Level)

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Speed is the rate of change of distance traveled with respect to time. (Scalar)

• Average speed: $\frac{\text{Total} \, \text{Distance}}{\text{Total} \, \text{Time}} \: = \: \frac{\Delta x}{\Delta t}$
• Instantaneous Speed: Rate of change of distance with respect to time at that instant = $\frac{dx}{dt}$

Velocity is the rate of change of its displacement with respect to time. (Vector)

• Average Velocity: $\frac{\text{Total} \, \Delta \, \text{in} \, \text{Displacement}}{\text{Total} \, \text{Time}} \: = \: \frac{\Delta s}{\Delta t}$
• Instantaneous Velocity: Rate of change of displacement with respect to time at that instant = $\frac{ds}{dt}$
• SI unit for speed and 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.

Acceleration of an object is the rate of change of its velocity with respect to time.

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

Average Acceleration: $a \, = \, \frac{v – u}{t}$

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

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