Cambridge IGCSE Physics

## Speed and velocity **Speed** is the distance travelled per unit time. For a steady speed, $$v = \frac{s}{t}$$ where $v$ is speed in $\mathrm{m\,s^{-1}}$, $s$ is distance in metres and $t$ is time in seconds. Most real trips have a speed that changes, so it is more useful to work with the **average speed**: $$\text{average speed} = \frac{\text{total distance travelled}}{\text{total time taken}}$$ **Velocity** is speed in a given direction. Two cars travelling at $20\,\mathrm{m\,s^{-1}}$ in opposite directions have the same speed but opposite velocities. Speed is a scalar and velocity is a vector (the difference is explained in the note on forces and vectors). A cyclist rides 1.2 km in 4.0 minutes and then 0.6 km in 2.0 minutes. The total distance is 1 800 m and the total time is 6.0 minutes, which is 360 s, so the average speed is $1800 \div 360 = 5.0\,\mathrm{m\,s^{-1}}$. Converting to SI units first avoids the most common slip, which is mixing kilometres with seconds. ## Acceleration **Acceleration** is the change in velocity per unit time. $$a = \frac{\Delta v}{\Delta t}$$ Here $\Delta v$ is the change in velocity in $\mathrm{m\,s^{-1}}$, $\Delta t$ is the time taken in seconds and $a$ is in $\mathrm{m\,s^{-2}}$. A vehicle that speeds up from $4\,\mathrm{m\,s^{-1}}$ to $16\,\mathrm{m\,s^{-1}}$ in $3.0\,\mathrm{s}$ has $a = 12 \div 3.0 = 4.0\,\mathrm{m\,s^{-2}}$. A **deceleration** is a negative acceleration: the velocity is getting smaller in the direction of travel. A…