A scalar quantity, such as distance, speed, mass, energy, temperature and time, has magnitude but no specific direction. Vector quantities, such as force, velocity, displacement, weight, acceleration and momentum, have a magnitude and a direction.
Speed is the rate a which an object moves. Its vector equivalent is velocity, the speed in a stated direction.
Distance – Time Graphs like the one above shows how far away an object has moved. The gradient at any one point is equal to the speed. To find the gradient of a curve, draw a tangent then work out the gradient of this.
Acceleration is the change in velocity in a certain amount of time. Constant acceleration is sometimes called uniform acceleration. Acceleration due to gravity is uniform for objects in freefall, roughly 10m/s2. This value is the same as the gravitational field strength
where a = Acceleration (m/s2), Δv = Change in Velocity (m/s) and t = Time (s)
Use the equation 
where v = Final Velocity (m/s), u = Initial Velocity (m/s), a = Acceleration (m/s2) and x = Distance (m)
Distance travelled = Area under a velocity-time graph
Speed can be measured using light gates, or a ruler and a stopwatch, or a video tape.
Typical speeds include:
• Walking 1.4m/s • On Motorways 31m/s
• Running 3m/s • Trains 55m/s
• Cycling 5.5m/s • Wind 5 – 20m/s
• Cars 13m/s • Sound 330m/s
Newton’s Laws and Momentum
Newton’s First Law states that an object will remain at rest or in uniform motion in one direction unless a resultant force acts upon it. The property of matter which causes the tendency of objects to move at a constant velocity is inertia. Inertia is the unwillingness of objects to change velocity and can be measured by its inertial mass, found by rearranging the formula derived from Newton’s Second Law
Newton’s Second Law states that Force is directly proportional to (α) Acceleration, and is summarised in the following equation:
Weight is the force acting on an object due to gravity, caused by the gravitational field around the Earth. Weight is measured using a calibrated spring balance or a newton meter.
An object moving in a circular orbit at constant speed is accelerating as it is changing direction, so there is a change in velocity. Acceleration is defined as the change in velocity over a period of time. There must be a resultant force acting on the object that keeps it moving, and acts towards the centre of the circle. This force is called centripetal force
Newton’s Third Law states that every action has an equal and opposite reaction. For an object in equilibrium, the force acting in one direction, e.g. the weight, is equal to the normal reaction force.
Momentum is the tendency of an object to keep moving in the same direction
Momentum is always conserved in a closed system and therefore in collisions the total momentum of the moving objects is conserved and shared among the components that experience the resultant force, as there will be an equal and opposite force on the stationary and moving objects
Use the equation:
where F = Force (N), m = Mass (kg), (v-u) = Change in Speed (m/s) and t = Time (s). This equation is found from Newton’s Second Law
CORE PRACTICAL: Investigating Motion
A – Set up light gates to measure speed, and connect to data logger
B – Prop up one end of the ramp to remove the impact of friction on the results
C – Place a trolley with a piece of card on the ramp, connected to masses applying a weight force
D – Allow the trolley to move down the ramp. The card will move through the light gates and the data logger will display the acceleration
E – Change the force applied and repeat. Once finished, draw a graph of acceleration against force. The variables of force and acceleration are in direct proportion, as a result of Newton’s Second Law
Car Safety
- The Ruler Drop Experiment is used to measure times. Results are usually 0.2 – 0.6s. Typically, an alert driver has a reaction time of 1s
- Thinking Distance is the distance travelled in the driver’s reaction time, affected by the reaction time, to which tiredness, alcohol, drugs and distraction contribute, and also the speed of the car
- Braking Distance is the distance taken to stop once the brakes have been applied and the car is decelerating. It is affected by speed, mass of the car and its contents, the condition of the brakes, the state of the road and the amount of friction between the tyres and the road
- The braking distance depends on the initial velocity’s value squared. This is because the word done by the brakes is equal to the original kinetic energy of the car.
- At 30mph, the braking distance is 23m, at 50mph it is 53m and at 70mph it is 75m. On a road there is a force of friction between the tyres and the road, and also a weight force of the car on the road
where d = Braking Distance, m = Mass of Car (kg), v = Initial Velocity of Car (m/s) and F = Force Applied by Brakes (N)
Large decelerations can cause serious injury, as passengers experience great forces due to the change in momentum. The force can be lowered by slowing the object down over a long time.
- Safety features in vehicles are designed to increase collision times, which reduces the force, so reduces risk of injury.
- Seatbelts stop the passengers from flying, and stretch during a collision. This increases the time taken for the body’s momentum to reach zero, so reduces the force on it.
- Air bags increase the time taken for momentum to reach zero as they expand very rapidly, meaning the head is slowed from reaching the dashboard as it must compress the air. This feature also prevents major trauma to the head as the blow is cushioned.
- Crumple zones crush during a collision in a controlled way, increasing the time taken for momentum to be transferred
- Brakes transfer energy to the vehicle’s kinetic energy store from the thermal store of the brakes. Very large decelerations cause the brake to overheat and make the vehicle skid