Class 9 Science Chapter 4: Describing Motion Around Us — Notes, Examples & Practice

An object is in motion if its position changes with time relative to a reference point (origin). Rest and motion are relative: a passenger in a moving bus is at rest relative to the bus but moving relative to the road.

Distance is the total length of the path travelled. It has only size (magnitude), so it is a scalar. Displacement is the shortest straight-line change in position from start to finish, with direction, so it is a vector.

Displacement can be zero even when distance is not — run one full lap of a 400 m track and your distance is 400 m but your displacement is 0. The magnitude of displacement is never greater than the distance.

Speed is distance travelled per unit time. Average speed $= \dfrac{\text{total distance}}{\text{total time}}$. Its SI unit is m/s; km/h is common in daily life.

Velocity is speed in a given direction: average velocity $= \dfrac{\text{displacement}}{\text{time}}$. It is a vector and can be negative (moving in the negative direction).

Motion is uniform if equal distances are covered in equal intervals of time (in a straight line, this means constant velocity) and non-uniform otherwise. When velocity changes uniformly, average velocity $= \dfrac{u + v}{2}$.

Acceleration is the rate of change of velocity: $a = \dfrac{v - u}{t}$, where $u$ is the initial velocity and $v$ the final velocity after time $t$. Its SI unit is m/s² (metres per second, per second).

If velocity increases in the direction of motion, acceleration is positive. If it decreases, acceleration is negative — called retardation or deceleration (a braking car).

Velocity also changes when direction changes. So an object moving in a circle at constant speed is accelerating — its velocity keeps turning. Uniform acceleration means equal changes in velocity in equal time intervals, such as a freely falling stone (about 9.8 m/s² downward).

On a distance–time (or position–time) graph, the slope gives the speed (velocity). A straight sloping line = uniform motion; a steeper line = faster; a horizontal line = at rest; a curve = changing speed.

On a velocity–time graph, the slope gives the acceleration, and the area under the graph gives the displacement. A horizontal line = constant velocity; a straight sloping line = uniform acceleration; a line going down = retardation.

Read graphs carefully: check the axes, the units and the scale first. A graph is not a picture of the path — a straight line on a d–t graph does not mean the road is straight.

For motion in a straight line with uniform acceleration, three equations connect $u$ (initial velocity), $v$ (final velocity), $a$ (acceleration), $t$ (time) and $s$ (displacement).

They come straight from the v–t graph: the slope gives $v = u + at$; the area of the trapezium gives $s = ut + \dfrac{1}{2}at^2$; eliminating $t$ gives $v^2 = u^2 + 2as$.

Choose the equation that contains the three quantities you know and the one you want. Pick a positive direction and keep signs consistent. These equations do not apply when acceleration is changing.