Physics on the Move
Speed, Distance and Time
The OCR Gateway specification requires you to know typical speeds for everyday scenarios: walking (~1.5 m/s), running (~3 m/s), cycling (~6 m/s), cars in town (~13 m/s or 30 mph), motorway driving (~30 m/s or 70 mph), speed of sound in air (~340 m/s), and wind speeds which vary widely (P6.1a).
Speed is the distance travelled per unit time. The equation is:
$$\text{speed} = \frac{\text{distance}}{\text{time}} \quad \text{or} \quad v = \frac{s}{t}$$
where \(v\) = speed in m/s, \(s\) = distance in metres, \(t\) = time in seconds. Speed can also be measured in km/h for longer journeys.
Speed = distance ÷ time (\(v = s/t\)). Typical speeds: walking 1.5 m/s, running 3 m/s, cycling 6 m/s, car on motorway 30 m/s, sound in air 340 m/s.
Velocity and Acceleration
Velocity is speed in a given direction. It is a vector quantity (has both magnitude and direction), while speed is a scalar (magnitude only). An object moving in a circle at constant speed has a changing velocity because its direction is constantly changing.
Acceleration is the rate of change of velocity (PM2.1ii):
$$a = \frac{v - u}{t}$$
where \(a\) = acceleration in m/s\(^2\), \(v\) = final velocity, \(u\) = initial velocity, \(t\) = time. Positive acceleration means speeding up; negative acceleration (deceleration) means slowing down.
Example: a car accelerates from rest (\(u = 0\)) to 20 m/s in 8 seconds. Acceleration = \(\frac{20 - 0}{8} = 2.5\) m/s\(^2\). If the same car then brakes from 20 m/s to rest in 4 seconds, the deceleration = \(\frac{0 - 20}{4} = -5\) m/s\(^2\). The negative sign indicates slowing down.
An object in free fall near the Earth’s surface accelerates at approximately \(9.8\) m/s\(^2\) (often rounded to \(10\) m/s\(^2\) for calculations). This is the acceleration due to gravity, denoted \(g\). In the absence of air resistance, all objects fall at the same rate regardless of their mass — a key insight from Galileo’s experiments.
The relationship between force, mass and acceleration (Newton’s Second Law) can also be written as \(a = \frac{F}{m}\), showing that for a given force, a heavier object accelerates less. This explains why a fully loaded lorry takes much longer to stop than an empty car travelling at the same speed — both the greater mass and the greater kinetic energy (\(KE = \frac{1}{2}mv^2\)) increase the braking distance.
Distance-time graphs show how far an object has travelled over time (P2.1e). A straight line means constant speed; a steeper gradient means faster speed. A horizontal line means the object is stationary. A curve means the speed is changing (accelerating or decelerating). The gradient of the line equals the speed.
Velocity-time graphs show how velocity changes over time. A horizontal line means constant velocity. A positive gradient means acceleration; a negative gradient means deceleration. The area under the line equals the distance travelled. A steeper gradient means greater acceleration.
To calculate the area under a velocity-time graph for irregular shapes, split it into rectangles and triangles. Area of a triangle = \(\frac{1}{2} \times \text{base} \times \text{height}\).
Distance-time graphs: gradient = speed. Velocity-time graphs: gradient = acceleration, area under graph = distance. Straight lines = constant speed or constant acceleration.
Reaction Time and Stopping Distance
Reaction time is the delay between seeing a hazard and responding. Typical human reaction time is 0.2–0.9 seconds. Factors that increase reaction time include tiredness, alcohol, drugs, distractions and age.
Stopping distance = thinking distance + braking distance (P6.1e). Thinking distance is the distance travelled during the driver’s reaction time. Braking distance is the distance travelled once the brakes are applied. Factors increasing braking distance include wet or icy roads, worn tyres, worn brakes and higher speed. At higher speeds the car has more kinetic energy, so the brakes must transfer more energy to heat and the car travels further before it stops.
Newton’s First Law: an object at rest stays at rest, and an object in motion stays at constant velocity, unless acted on by a resultant (unbalanced) force.
Newton’s Second Law: \(F = m \times a\) — the resultant force on an object equals its mass times its acceleration. A larger force produces a larger acceleration; a larger mass reduces the acceleration for the same force.
Newton’s Third Law: for every action force, there is an equal and opposite reaction force. These act on different objects.
When an object falls, it initially accelerates due to gravity. As speed increases, air resistance increases until it equals the gravitational force. At this point, the resultant force is zero and the object reaches terminal velocity — falling at a constant speed.
Stopping distance = thinking distance + braking distance. Newton’s Second Law: \(F = ma\). At terminal velocity, air resistance equals weight and acceleration is zero.