Kinematics

Kinematics starts by distinguishing between scalar and vector quantities. A scalar has magnitude (size) only, like distance and speed. A vector has both magnitude and direction, like displacement and velocity. Distance is the total length of the path travelled, regardless of direction. Displacement(s) is the object's overall change in position, measured as a straight line from the start point to the end point, including direction. Similarly, speed is a scalar measure of how fast an object is moving (rate of change of distance), while velocity(v) is a vector measure of the rate of change of displacement. Two objects can have the same speed but different velocities if they are moving in different directions.

Acceleration(a) is the rate of change of velocity. It is a vector quantity, measured in metres per second squared (m/s²). An object is accelerating if it is speeding up, slowing down (decelerating), or changing direction. For motion in a straight line with constant (uniform) acceleration, we can use a set of five special equations known as the SUVAT equations. The variables are: s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time. To solve a problem, you identify three known variables and use the appropriate equation to find the unknown.

Graphs are powerful tools for visualising and analysing motion. The three main types are displacement-time (s-t), velocity-time (v-t), and acceleration-time (a-t) graphs. For a displacement-time graph, the gradient (slope) of the line gives the velocity. A straight line means constant velocity, while a curve means acceleration. For a velocity-time graph, the gradient gives the acceleration, and the area under the graph gives the displacement. A horizontal line means constant velocity (zero acceleration), a straight sloping line means constant acceleration, and a curve means non-uniform acceleration. For an acceleration-time graph, the area under the graph gives the change in velocity.

A projectile is any object that is thrown and moves under the influence of gravity alone (air resistance is usually ignored in initial problems). The key to solving projectile motion problems is to treat the horizontal and vertical components of the motion completely independently. The horizontal motion has constant velocity (acceleration is zero). The vertical motion has constant downward acceleration, which is the acceleration due to gravity, g (≈ 9.81 m/s²). You use the standard SUVAT equations for the vertical component and the simple `distance = speed × time` equation for the horizontal component. The time of flight is the link that connects the two components.

In real-world situations, a fluid resistance force, such as air resistance, opposes the motion of an object. This force is not constant; it increases as the object's speed increases. For a projectile, air resistance reduces its maximum height and range, and makes the flight path asymmetrical (the descent is steeper than the ascent). For a falling object, like a skydiver, air resistance increases as they speed up. Eventually, the upward force of air resistance becomes equal in magnitude to the downward force of weight. At this point, the net force on the object is zero, so its acceleration becomes zero. The object stops accelerating and falls at a constant maximum speed, known as terminal velocity.