A.1 Kinematics

Quantities

• Displacement s (vector, m) is the straight-line change in position; distance is a scalar.
• Velocity v = Δs / Δt (vector); speed is a scalar.
• Acceleration a = Δv / Δt (vector, m s⁻²).

Uniformly accelerated motion (constant a, straight line)

• v = u + at
• s = ut + ½at²
• v² = u² + 2as
• s = ½(u + v)t

Choose a positive direction first and keep the signs of u, v, a and s consistent with it.

Graphs

• Displacement against time: the gradient is the velocity.
• Velocity against time: the gradient is the acceleration and the area under the graph is the displacement.
• Acceleration against time: the area under the graph is the change in velocity.

Projectile motion (no air resistance)

Treat the horizontal and vertical motions separately. Horizontally a = 0; vertically a = g = 9.81 m s⁻² downwards.

• Components: ux = u cos θ and uy = u sin θ.
• At the highest point vy = 0 but vx is unchanged, so the speed is not zero.
• Time of flight on level ground: T = 2u sin θ / g.
• Maximum height: H = u² sin² θ / (2g). Range on level ground: R = u² sin 2θ / g.

Fluid resistance

Drag grows with speed. A falling object reaches terminal speed when the drag force equals its weight; the net force and the acceleration are then zero.