Measuring speed

1. Every speed method measures a distance and the corresponding time, then uses
2. $$average\; speed=\frac{distance}{time}$$
3. For a stopwatch method, mark two positions a measured distance apart. Time the object between the markers, repeat the measurement and calculate a mean.
4. A long measured distance reduces the percentage uncertainty in the distance and makes reaction-time uncertainty a smaller fraction of the measured time.

Using light gates

1. Attach a card of measured length to the moving object. Connect a light gate to a timer or data logger.
2. As the card passes through the beam, the logger measures the interruption time. The instantaneous speed at the gate is approximated by
3. $$v=\frac{card\; length}{interruption\; time}$$
4. With two light gates, measure their separation and the travel time between them to calculate average speed over that interval.
5. Light gates remove the delay caused by starting and stopping a handheld stopwatch, so they reduce reaction-time uncertainty.

Other laboratory methods

1. A ticker timer makes dots on a moving tape at equal time intervals. Measure the distance across several intervals and divide by their total time.
2. If the mains frequency is $50Hz$, successive dots are separated by $\frac{1}{50}=0.020s$. Increasing gaps show increasing speed.
3. Video analysis uses a known scale in the frame and the recording frame rate. Measure the displacement across a known number of frames and divide by the elapsed time.
4. Motion sensors can record distance at short regular intervals. The gradient of a distance–time graph then gives speed.

Typical speeds

1. Typical values are estimates that provide an order-of-magnitude check rather than exact constants.
2. Walking is about $1.5m/s$, running about $3m/s$ and cycling about $6m/s$.
3. A car in urban traffic is about $13m/s$, which is roughly $30mph$, while motorway travel is about $30m/s$.
4. A train may travel at about $50m/s$ and a cruising passenger aircraft at about $250m/s$.
5. A gentle breeze is about $5m/s$ and a gale about $20m/s$.
6. Sound in air travels at about $330m/s$.
7. Useful conversions are $1m/s=3.6km/h$ and $1m/s\approx 2.2mph$.

Free-fall acceleration

1. Near the Earth’s surface, the acceleration in free fall is
2. $$g=10{m/s}^2$$
3. The acceleration is directed downwards towards the centre of the Earth. An object’s downward velocity therefore increases by about $10m/s$ each second when air resistance is negligible.
4. All objects have the same free-fall acceleration at the same location, regardless of mass. A greater mass produces a proportionally greater weight, so $a=F/m$ remains the same.
5. A ball thrown upwards is still accelerating downwards. It slows while rising, has zero instantaneous velocity at its highest point, then speeds up downwards.
6. The symbol $g$ can also represent gravitational field strength in $N/kg$. The numerical value near Earth is also about $10$, but acceleration and field strength have different units.

Estimating accelerations

1. Use $a=\frac{v-u}{t}$ with sensible estimates for the velocity change and time interval.
2. A train leaving a station may accelerate at about $0.5{m/s}^2$, a car pulling away at about $2{m/s}^2$ and a sprinter at about $5{m/s}^2$.
3. Hard braking can produce a deceleration with magnitude approaching $10{m/s}^2$.
4. Check that the estimate matches the context and quote an appropriate unit and sensible precision.