Motion and Time

What you'll learn

Speed: definition, formula, units.
Uniform vs non-uniform motion.
Distance-time graphs — how to read and draw them.
Simple pendulum — what determines its time period.
Units of time and measuring time accurately.

Key concepts

Distance, speed and time

Distance: total path length covered.
Speed: distance covered per unit time.

Speed = Distance / Time v = d / t

Unit: m/s (SI), also km/h.
Conversion: 1 km/h = 1000/3600 m/s = 5/18 m/s; 1 m/s = 18/5 km/h = 3.6 km/h.

Quantity	Symbol	Unit
Distance	d	m (metres)
Speed	v	m/s
Time	t	s (seconds)

Examples:

A car covers 120 km in 2 hours. Speed = 120/2 = 60 km/h = 50/3 m/s ≈ 16.7 m/s.
A cyclist travels at 5 m/s for 10 s. Distance = 5 × 10 = 50 m.

Types of motion

Type	Description	Speed	Example
Uniform motion	Equal distance in equal time intervals	Constant speed	Train on straight track; light
Non-uniform motion	Unequal distances in equal time intervals	Changing speed	Car in traffic; falling object

Uniform motion: no acceleration; distance-time graph is a straight line.
Non-uniform motion: accelerating or decelerating; distance-time graph is a curve.

Distance-time graphs

Interpreting distance-time graphs:

Graph shape	What it means
Horizontal line (flat)	Object is stationary (at rest)
Straight line sloping upward	Uniform motion (constant speed); steeper slope = faster speed
Curved line sloping upward	Non-uniform motion — speed is changing
Downward sloping line	Object returning (moving toward starting point)

Reading speed from a distance-time graph:

Speed = gradient (slope) of the line = rise/run = Δd/Δt.
Steeper slope → higher speed.

Plotting a distance-time graph:

Time on X-axis; Distance on Y-axis.
Plot (time, distance) data points.
Join points smoothly.
Read slope for speed.

Units of time

Unit	Value
Second (s)	SI unit of time
Minute (min)	60 s
Hour (h)	3600 s
Day	86,400 s

Periodic motion: motion that repeats after fixed intervals (oscillation of a pendulum, Earth's rotation).
Time measuring devices: sundial (ancient), water clock (clepsydra), hourglass, mechanical clock, quartz clock, atomic clock (most accurate — used in GPS; accurate to 1 second in 300 million years).

Simple pendulum

A simple pendulum consists of a small heavy mass (bob) attached to a long, light string, fixed at one end; free to swing.
One oscillation (one complete swing): from one extreme to the other and back again.
Time period (T): time for one complete oscillation.

What affects the time period?

Factor	Effect on T	Explanation
Length of string (L)	Longer string → longer T	More distance to travel
Acceleration due to gravity (g)	Higher g → shorter T	Stronger pull speeds up swing
Amplitude (swing angle)	No effect (for small angles < 15°)	Galileo discovered this — isochronous property
Mass of bob	No effect	Heavier bob doesn't swing faster or slower

T = 2π√(L/g) (for small angles)

A pendulum with L = 1 m on Earth (g = 9.8 m/s²): T ≈ 2 s.
Seconds pendulum: T = 2 s; L = ~1 m.

Applications of pendulums:

Grandfather/pendulum clocks — pendulum keeps time.
Seismographs — measure earthquakes.
Foucault's pendulum — demonstrates Earth's rotation.

Galileo and the pendulum:

Galileo Galilei (1564–1642) observed a swinging chandelier in Pisa Cathedral.
Used his own pulse to time swings — discovered time period depends only on length, not amplitude or mass.

Measuring time accurately

Stopwatch: measures time to 0.1 s (mechanical) or 0.01 s (digital).
Best practice: measure 10 or 20 oscillations and divide by number for accurate T.
Human reaction time (~0.2 s) introduces error in single measurements.

Quick check

A train covers 300 km in 5 hours. What is its speed in km/h and m/s?
What does a horizontal line on a distance-time graph indicate?
What is a simple pendulum? What is its time period?
Will a pendulum with twice the length have twice the time period? Explain.
How would you find the speed of an object from a distance-time graph?

Open the Practice tab for graded questions on Motion and Time.

Motion & Time