Introduction
Everything around us is in motion — planets orbit stars, blood flows in our veins, and atoms vibrate. Physics begins by describing this motion precisely. In this chapter you will learn about distance, displacement, speed, velocity, acceleration, and how to use motion graphs and equations.
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Key Concepts
1. Rest and Motion
An object is at rest if its position does not change with time relative to a reference point. It is in motion if its position changes. Rest and motion are relative — the same object can be at rest relative to one observer and in motion relative to another.
- 2. Distance and Displacement
- Distance: total path length covered; a scalar quantity (magnitude only). Symbol: d or s. Unit: metre (m).
- Displacement: shortest straight-line path from start to finish with direction; a vector quantity. Symbol: x or s. Unit: metre (m).
- 3. Speed and Velocity
- Speed = distance / time (scalar). Unit: m/s.
- Velocity = displacement / time (vector). Unit: m/s.
- Average speed = total distance / total time
- Uniform speed: equal distances in equal time intervals.
- Non-uniform speed: unequal distances in equal time intervals.
- 4. Acceleration
- Rate of change of velocity.
- a = (v - u) / t
- u = initial velocity, v = final velocity, t = time
- Unit: m/s2
- Positive acceleration: speeding up. Negative acceleration (deceleration/retardation): slowing down.
- 1.5. Equations of Motion (for uniform acceleration in a straight line)
- 2.v = u + at
- 3.s = ut + (1/2)at2
- 4.v2 = u2 + 2as
- 6. Distance-Time and Velocity-Time Graphs
- Distance-time graph:
- Straight line through origin = uniform speed; slope = speed
- Horizontal line = object at rest
- Curve = non-uniform speed
- Velocity-time graph:
- Straight horizontal line = uniform velocity (zero acceleration)
- Straight line sloping up = uniform acceleration; slope = acceleration
- Area under v-t graph = displacement
7. Uniform Circular Motion
An object moving in a circle at constant speed has changing velocity (direction changes), so it undergoes acceleration (centripetal acceleration directed toward the centre). Speed is constant but velocity is not.
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Worked Examples
A car travels 60 km in 1.5 hours. Calculate its average speed in m/s.
Speed = 60 km / 1.5 h = 40 km/h. Convert: 40 x (1000/3600) = 40 x 5/18 = 11.11 m/s
A ball starts from rest and accelerates uniformly at 2 m/s2 for 5 seconds. Find its final velocity.
u = 0, a = 2 m/s2, t = 5 s. v = u + at = 0 + 2 x 5 = 10 m/s
Using Example 2, find the distance covered.
s = ut + (1/2)at2 = 0 x 5 + (1/2) x 2 x 25 = 0 + 25 = 25 m
A train moving at 20 m/s decelerates at 4 m/s2. How far does it travel before stopping?
u = 20 m/s, v = 0, a = -4 m/s2. v2 = u2 + 2as: 0 = 400 + 2(-4)s: 8s = 400: s = 50 m
A distance-time graph shows a horizontal straight line. What does this indicate?
A horizontal line means distance is not increasing with time — the object is at rest.
A velocity-time graph shows a straight line from (0, 5) to (10, 25). Calculate acceleration and displacement.
Acceleration = slope = (25 - 5) / (10 - 0) = 20/10 = 2 m/s2
Displacement = area under graph = area of trapezium = (1/2)(5 + 25) x 10 = (1/2)(30)(10) = 150 m
Is a satellite in a circular orbit at constant speed accelerating? Explain.
Yes. Although its speed is constant, its direction changes continuously. Velocity is a vector (speed + direction). Changing direction means changing velocity, which means the satellite is accelerating (centripetal acceleration toward Earth).
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Common mistakes
- Confusing distance (scalar, total path) with displacement (vector, shortest straight-line path).
- Assuming uniform circular motion has zero acceleration — it does not; direction of velocity changes constantly.
- Forgetting that the area under a velocity-time graph gives displacement, not distance (unless speed is always positive).
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Summary
Motion is described using distance, displacement, speed, velocity, and acceleration. The three equations of motion (v = u + at; s = ut + (1/2)at2; v2 = u2 + 2as) apply to uniform acceleration. Distance-time and velocity-time graphs are powerful tools for analysing motion. Uniform circular motion involves constant speed but continuously changing velocity, making it an accelerated motion.