Motion is all around us. The Earth revolves around the Sun, birds fly, cars move on roads, and even the air around us is in motion. An object is said to be in motion if its position changes with time with respect to its surroundings. If the position of an object does not change with time, the object is said to be at rest. Motion and rest are relative - a person sitting in a moving train is at rest with respect to the train but in motion with respect to the trees outside.
The study of motion is called mechanics, and the branch of mechanics that describes how objects move without considering the forces causing the motion is called kinematics. In this chapter we study distance and displacement, speed and velocity, acceleration, and the equations of motion for uniformly accelerated motion.
We will also learn to represent motion graphically using distance-time and velocity-time graphs, and understand the motion of an object falling freely under gravity.
To describe the motion of an object, we need a reference point and a coordinate system. Motion can be along a straight line (rectilinear motion), along a circular path (circular motion), or along a curved path. The simplest type of motion to study is motion along a straight line.
Distance: The distance travelled by an object is the total length of the path covered by it. Distance is a scalar quantity - it has only magnitude and no direction. The SI unit of distance is the metre (m). Distance is always positive.
Displacement: Displacement is the shortest distance from the initial position to the final position of the object, in a particular direction. Displacement is a vector quantity - it has both magnitude and direction. The displacement of an object can be zero even when it has travelled a distance. For example, if a body moves from point A to B and returns to A, the distance covered is 2AB but the displacement is zero.
The SI unit of displacement is the metre, and it can be positive, negative or zero.
If an object covers equal distances in equal intervals of time, its motion is called uniform motion. For example, if a car travels 10 km in every 15 minutes, its motion is uniform.
If an object covers unequal distances in equal intervals of time, its motion is called non-uniform motion. For example, a car moving in heavy traffic covers different distances in equal intervals of time.
The motion of most objects in daily life is non-uniform.
Speed: Speed is the distance travelled by an object per unit time. It is a scalar quantity.
Speed = Distance travelled / Time taken
The SI unit of speed is metre per second (m/s). Other units are centimetre per second (cm/s) and kilometre per hour (km/h). Note that 1 km/h = 5/18 m/s, and 1 m/s = 18/5 km/h.
Average speed: The average speed of an object is the total distance travelled divided by the total time taken. If the speed of an object changes with time, we use average speed.
Average speed = Total distance travelled / Total time taken
Velocity: Velocity is the displacement of an object per unit time. It is a vector quantity.
Velocity = Displacement / Time taken
The SI unit of velocity is m/s. When the motion is in one direction, the magnitude of velocity equals the speed. The velocity of an object can change if its speed changes, if its direction changes, or if both change.
Average velocity: If the velocity changes uniformly, the average velocity is the arithmetic mean of the initial velocity (u) and final velocity (v):
Average velocity = (u + v) / 2
Acceleration is the rate of change of velocity of an object. Since velocity is a vector quantity, acceleration is also a vector quantity.
Acceleration = Change in velocity / Time taken = (v - u) / t
The SI unit of acceleration is m/s^2. If the velocity of an object increases, the acceleration is positive; if the velocity decreases, the acceleration is negative, and it is called deceleration or retardation.
When a car starts from rest, its velocity increases and it has positive acceleration. When brakes are applied, the velocity decreases and the car has negative acceleration (retardation). If the velocity does not change, the acceleration is zero and the body is said to be moving with uniform velocity.
Motion can be represented graphically, which makes it easier to study.
Distance-time graph: The distance is taken on the Y-axis and time on the X-axis. For uniform motion, the distance-time graph is a straight line passing through the origin, and its slope gives the speed of the object. For non-uniform motion, the distance-time graph is a curved line.
Velocity-time graph: The velocity is taken on the Y-axis and time on the X-axis. For uniform velocity, the velocity-time graph is a straight line parallel to the time axis. The area under a velocity-time graph gives the displacement of the object. The slope of a velocity-time graph gives the acceleration.
For a body moving with uniform acceleration, the velocity-time graph is a straight line inclined to the time axis.
For a body moving with uniform acceleration, there are three equations of motion. Here u is the initial velocity, v is the final velocity, a is the acceleration, t is the time and s is the displacement.
First equation of motion: v = u + at
This equation relates velocity, acceleration and time.
Second equation of motion: s = ut + (1/2)at^2
This equation relates displacement, initial velocity, acceleration and time.
Third equation of motion: v^2 = u^2 + 2as
This equation relates velocity, acceleration and displacement.
These equations can be derived graphically or using calculus, and are used to solve problems of uniformly accelerated motion.
When an object moves along a circular path with a constant speed, its motion is called uniform circular motion. Even though the speed is constant, the velocity changes continuously because the direction of motion changes at every point. Hence, uniform circular motion is always an accelerated motion.
The acceleration associated with uniform circular motion is directed towards the centre of the circle and is called centripetal acceleration.
For example, the motion of the tip of the hands of a clock, the motion of a satellite around the Earth, and the motion of a stone tied to a string whirled around are examples of uniform circular motion.
| Quantity | Type | Formula | Unit |
|---|---|---|---|
| Distance | Scalar | Total path length | m |
| Displacement | Vector | Shortest distance with direction | m |
| Speed | Scalar | distance / time | m/s |
| Velocity | Vector | displacement / time | m/s |
| Acceleration | Vector | (v - u) / t | m/s^2 |
| Equation of Motion | Formula |
|---|---|
| First | v = u + at |
| Second | s = ut + (1/2)at^2 |
| Third | v^2 = u^2 + 2as |
In this chapter we learned to describe motion using the concepts of distance and displacement, speed and velocity, and acceleration. We distinguished between uniform and non-uniform motion and understood how velocity differs from speed. The equations of motion - v = u + at, s = ut + (1/2)at^2 and v^2 = u^2 + 2as - allow us to solve problems of uniformly accelerated motion. Graphical representation helped us see that the slope of a distance-time graph gives speed, the slope of a velocity-time graph gives acceleration, and the area under a velocity-time graph gives displacement. Finally, we understood that uniform circular motion, though uniform in speed, is accelerated because the direction of velocity keeps changing. These ideas form the foundation of the study of physics and are used extensively in the next chapters on force and gravitation.