Scalar and vector quantities, distance, displacement, speed, velocity and acceleration, distance-time and velocity-time graphs, the equations of motion, and the meaning of gradient and area under a graph.

What this topic is asking

OCR wants you to distinguish scalar and vector quantities, define and calculate speed, velocity and acceleration, interpret distance-time and velocity-time graphs, and use the equations of motion.

Scalars, vectors and the key quantities

The everyday quantities of motion are:

• Distance (scalar) is how far an object moves; displacement (vector) is the straight-line distance and direction from start to finish.
• Speed (scalar) is how fast an object moves: $\text{speed} = \dfrac{\text{distance}}{\text{time}}$. Typical speeds to know include walking at about $1.5$ m/s, running at about $3$ m/s, and a car on a motorway at around $30$ m/s.
• Velocity (vector) is the speed in a stated direction.
• Acceleration (vector) is the rate of change of velocity: $a = \dfrac{\Delta v}{t}$, the change in velocity divided by the time taken. Deceleration is a negative acceleration (slowing down).

Motion graphs

Graphs are a major part of this topic, and you must read them precisely.

To find a distance from a velocity-time graph, calculate the area under the line by splitting it into rectangles and triangles and adding them, or by counting squares. To find an acceleration, calculate the gradient as the change in velocity divided by the change in time over a straight section.

The equations of motion

For motion with uniform (constant) acceleration, OCR uses these relationships. Acceleration is $a = \dfrac{v - u}{t}$, where $u$ is the initial velocity and $v$ is the final velocity. A useful equation that does not need the time is:

where $s$ is the distance travelled. You can also find the distance from the average speed: $\text{distance} = \dfrac{u + v}{2} \times t$. These let you solve for any missing quantity given enough of the others, which is a common calculation in Paper 5.