Mechanics and Kinematics
Scalars, vectors and motion graphs
Kinematics describes motion without considering its causes. Distinguish scalars (distance, speed, mass, time) from vectors (displacement, velocity, acceleration, force). Average speed = total distance ÷ time; velocity is displacement ÷ time. On a displacement–time graph the gradient is velocity; on a velocity–time graph the gradient is acceleration and the area under the line is displacement. Area below the time axis represents negative displacement.
Uniform acceleration equations
For constant acceleration a: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t. Select the equation that omits the quantity not given. Choose one direction as positive and keep it throughout; g is 9.81 m/s² downward.
Projectiles
Resolve the initial velocity into horizontal and vertical components. Ignoring air resistance, horizontal acceleration is zero, so horizontal velocity is constant. Vertical acceleration is g downward. The time of flight is found from vertical motion; range = horizontal component × time.
Worked example
A ball is kicked at 20.0 m/s at 30° above horizontal from level ground. Find its range. ux = 20.0 cos 30° = 17.3 m/s; uy = 20.0 sin 30° = 10.0 m/s. Time to the top = uy/g = 10.0/9.81 = 1.02 s, so flight time = 2.04 s. Range = 17.3 × 2.04 = 35.3 m. The vertical motion fixes the time; the horizontal motion fixes the distance.
Traps
Mixing distance with displacement; forgetting that area below the time axis is negative displacement; using g = 10 when the data expect 9.81; treating a projectile’s horizontal velocity as changing; rounding intermediate values too early; failing to state the direction of a vector answer.