Introduction to Kinematics
Kinematics is the branch of physics that describes how objects move , without worrying about why they move. It gives us a precise mathematical language to analyse motion in terms of displacement, velocity, acceleration, and time.
Picture a sprinter at the starting line of a 100 m race. The gun fires, they accelerate from rest, and gradually reach top speed before crossing the finish line. Kinematics lets us answer questions like:
- How long did the acceleration phase last?
- What was the sprinter's top speed?
- How far did they travel while accelerating?
In this subtopic, we focus on motion in a straight line (one dimension) under constant acceleration , the simplest and most foundational case.
Kinematics: The study of motion in terms of displacement, velocity, acceleration, and time, without reference to the forces causing the motion.
Displacement (s): The change in position of an object in a specified direction. It is a vector quantity, measured in metres (m).
Velocity (v): The rate of change of displacement with respect to time. It is a vector quantity, measured in m s⁻¹.
Acceleration (a): The rate of change of velocity with respect to time. It is a vector quantity, measured in m s⁻².
In IB Physics, displacement, velocity, and acceleration are all vector quantities , they have both magnitude and direction. Speed and distance are the corresponding scalar quantities. Always be careful about sign conventions when working in one dimension.
The Four Kinematic Equations
When an object moves in a straight line with constant acceleration, its motion is completely described by five variables:
| Symbol | Quantity | Unit |
|---|---|---|
| displacement | m | |
| initial velocity | m s⁻¹ | |
| final velocity | m s⁻¹ | |
| acceleration (constant) | m s⁻² | |
| time interval | s |
The four kinematic equations (also called the SUVAT equations) connect these variables. Each equation uses four of the five variables, so you choose the one that matches the information given in a problem.
v = u + at \tag{1}
s = ut + \frac{1}{2}at^2 \tag{2}
v^2 = u^2 + 2as \tag{3}
s = \frac{(u + v)}{2}\,t \tag{4}
SUVAT memory trick: Write out and cross out the variable that is absent from the problem. The equation that doesn't contain that variable is the one to use.
These equations are only valid when acceleration is constant throughout the motion. If acceleration varies with time, they cannot be applied directly.