Forces and Motion

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infoWhy this? Quantifying motion allows us to describe journeys, compare speeds, and explain how resultant forces change velocity. Calculations, force diagrams, and displacement–time graphs provide complementary ways to analyse speed, acceleration, relative motion, and direction.

scheduleWhy now? This unit develops the Year 7 account of balanced and unbalanced forces into a quantitative study of motion. Familiarity with force diagrams and resultants now supports calculations of speed and acceleration, preparing us for later work on energy transfers, work done, and kinetic energy.

Speed is defined as the distance travelled per unit time.
The equation for speed is speed equals distance divided by time, written as `v = \frac{d}{t}`.
Distance is measured in metres (m) and time in seconds (s) in standard SI units; speed is measured in metres per second (m/s).
Units for speed can also include kilometres per hour (km/h) or miles per hour (mph); compatible units must be used in calculations, and quantities need only be converted to SI units when an answer in SI units is required.
Larger units, such as kilometres and hours, are practical for large distances and times; smaller units, such as millimetres and seconds, are practical for small quantities.
A non-zero resultant force changes an object's velocity, causing acceleration, whereas balanced forces have a resultant force of zero and do not cause acceleration.
Acceleration is the change in velocity per unit time.
Acceleration can be calculated using the equation acceleration equals change in velocity divided by time taken, written as `a = \frac{\Delta v}{t}`.
A larger resultant force causes greater acceleration when the mass of the object is fixed.
The direction of the resultant force relative to an object's motion affects whether the object speeds up, slows down, or changes direction.
The resultant force is the single force that has the same effect as all the forces acting on an object combined.
When two forces act at right angles, the resultant force can be found using Pythagoras' theorem.
On a displacement–time graph, a straight, sloping line indicates constant velocity.
On a displacement–time graph, a horizontal line indicates that the object is stationary.
On a displacement–time graph, a greater gradient magnitude means a higher speed.
On a displacement–time graph, a negative gradient indicates motion in the negative direction and can represent an object returning towards its starting point.
On a displacement–time graph, a curved line indicates changing velocity, which may involve acceleration or deceleration.
The gradient of a displacement–time graph represents velocity, and speed is the magnitude of this gradient.
Relative speed is the speed of one object as observed from another moving object.

rocket_launchYou must be able to

Calculate speed, distance, or time using `v = \frac{d}{t}`, including rearranging the equation as needed.
Convert between different units of distance and time, such as kilometres to metres and hours to seconds, to ensure that compatible units are used in calculations.
Solve speed–distance–time problems in a variety of familiar and unfamiliar contexts, including those involving mixed units.
Measure the time taken for an object to travel a set distance using a stopwatch or other timing device.
Describe and carry out a method to determine the speed of an object experimentally.
Calculate speed from experimental data, including using average values where appropriate.
Draw displacement–time graphs to represent simple journeys in one direction and journeys involving a return to the starting point.
Interpret displacement–time graphs to identify when an object is stationary or moving in the positive or negative direction and to determine its displacement at a given time.
Calculate the velocity of an object from the gradient of a straight-line section of a displacement–time graph and calculate its speed from the magnitude of this gradient.
Interpret curved displacement–time graphs to identify acceleration or deceleration.
Calculate the relative speed of two objects travelling in opposite directions.
Calculate the time and distance at which two objects travelling towards each other will pass.
Calculate acceleration from the change in velocity and the time taken using `a = \frac{\Delta v}{t}`.
Calculate the resultant force when two forces act at right angles using Pythagoras' theorem.
Draw accurate force diagrams, including representing forces with arrows to scale and at the correct angles.
Explain, using diagrams and calculations, how the direction and size of resultant forces affect an object's motion.

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