Slow or fast?
If two runners start together, the one who covers the same distance in less time is faster. Or, if they run for the same time, the one who covers more distance is faster. Both ideas are captured by speed.
Speed
Speed is the distance covered per unit time.
Speed = distance covered ÷ time taken
The SI unit of speed is metres per second (m/s).
Vehicles use kilometres per hour (km/h).
To convert km/h to m/s, multiply by 1000/3600, which is 5/18. So 72 km/h = 72 × 5/18 = 20 m/s.
Example. A bus travels 120 km in 2 hours. Its speed is 120 ÷ 2 = 60 km/h.
Rearranging the formula: distance = speed × time, and time = distance ÷ speed.
Example. How long does a car moving at 50 km/h take to cover 175 km? Time = 175 ÷ 50 = 3.5 hours.
Uniform and non-uniform motion
Uniform motion: an object moving in a straight line covers equal distances in equal intervals of time. Its speed is constant.
Non-uniform motion: the speed keeps changing. A car in city traffic is in non-uniform motion.
For non-uniform motion, the formula gives the average speed: total distance ÷ total time.
Measuring time
Ancient people measured time with sundials, water clocks and sand clocks (hourglasses). Modern clocks and watches use periodic motion: motion that repeats itself at regular intervals.
A simple pendulum is a small metal ball (the bob) hung by a thread from a fixed point. When pulled to one side and released, it swings to and fro. This is called oscillatory motion.
One oscillation is a complete to-and-fro swing: from one extreme position to the other and back.
The time taken for one oscillation is the time period.
A pendulum of a given length has a constant time period. Galileo noticed this by watching a swinging lamp in a church, and it was later used to build pendulum clocks. Quartz clocks, which use the regular vibrations of a crystal, are far more accurate.
Units of time: the SI unit is the second (s). 60 seconds = 1 minute; 60 minutes = 1 hour.
Speedometer and odometer
The dashboard of a vehicle has two meters:
The speedometer shows the speed at that moment, in km/h.
The odometer shows the total distance the vehicle has travelled.
Distance-time graphs
Plot time on the horizontal (x) axis and distance on the vertical (y) axis.
Shape of the graph | What it means |
|---|---|
a straight sloping line | uniform motion (constant speed) |
a steeper straight line | a higher constant speed |
a horizontal line | the object is at rest (distance not changing) |
a curved line | non-uniform motion |
Example. A car covers 0 km at 0 h, 40 km at 1 h, 80 km at 2 h and 120 km at 3 h. The points lie on a straight line, so the motion is uniform, at 40 km/h.
Choose a scale that makes the graph fill most of the graph paper, for example 1 cm = 10 km on the distance axis.
Summary
Speed = distance ÷ time; units are m/s or km/h, and 1 km/h = 5/18 m/s.
Uniform motion has constant speed; for non-uniform motion we use average speed.
A pendulum has a constant time period, the basis of pendulum clocks.
On a distance-time graph, a straight line means constant speed and a flat line means rest.