Kinematics — OCR A-Level Physics
Test yourself on Kinematics with OCR A-Level practice questions.
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Kinematics explained
Kinematics distinguishes five quantities.
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Displacement is the straight-line distance in a stated direction from start to finish, so it is a vector and can be zero after a round trip. Instantaneous speed is the magnitude of velocity at one instant, found from the gradient of a distance–time graph or a tangent. Average speed is total distance divided by total time, a scalar. Velocity is displacement divided by time, a vector, so direction matters. Acceleration is the rate of change of velocity, a vector, and occurs whenever speed, direction or both change. For example, a car returning to its start has zero displacement but non-zero average speed.
(b) graphical representations of displacement, speed, velocity and acceleration
Motion graphs show how displacement, speed, velocity or acceleration vary with time. On a displacement–time graph, the gradient gives velocity, so a horizontal line means rest and a straight sloping line means constant velocity. On a velocity–time graph, the gradient gives acceleration and the area between the line and the time axis gives displacement. Speed–time graphs give distance from area but lose direction. Acceleration–time graphs show how acceleration changes; the area under them gives velocity change. Always read the axis labels and units first, because the same shape means different things on different graphs.
(c) Displacement–time graphs; velocity is gradient
A displacement–time graph plots displacement on the vertical axis against time on the horizontal axis. The gradient at any point equals the velocity at that time. A straight line means constant velocity; a horizontal line means zero velocity; a curve means changing velocity, so the gradient of a tangent gives the instantaneous velocity. A negative gradient means motion in the negative direction. For example, a line rising 20 m in 4 s has gradient 20 m ÷ 4 s = 5 m s⁻¹. Average velocity is the overall gradient between two points, while instantaneous velocity uses the tangent at one point.
(d) Velocity–time graphs; acceleration is gradient; displacement is area under graph.
A velocity–time graph plots velocity on the vertical axis against time on the horizontal axis. The gradient of the line gives acceleration: a = Δv/Δt, so a straight line means constant acceleration, a horizontal line means zero acceleration, and a curve means changing acceleration. The area between the graph line and the time axis gives displacement; areas above the axis are positive and areas below are negative, so total displacement is the signed sum. For example, a line rising from 0 m s⁻¹ to 20 m s⁻¹ in 4 s has gradient 5 m s⁻² and area 40 m. Split complex shapes into triangles, rectangles and trapezia, and use the correct units throughout.
Your focus
- Define displacement, instantaneous speed, average speed, velocity and acceleration.
- Classify each quantity as scalar or vector.
- Calculate average speed and velocity from distance, displacement and time.
Show all 12 objectives
- Interpret displacement–time, speed–time, velocity–time and acceleration–time graphs.
- Determine velocity from a displacement–time gradient and acceleration from a velocity–time gradient.
- Find displacement or velocity change from the appropriate area.
- Find velocity from the gradient of a displacement–time graph.
- Distinguish constant, zero and changing velocity from graph shape.
- Use a tangent to estimate instantaneous velocity on a curve.
- Determine acceleration from the gradient of a velocity–time graph.
- Determine displacement from the area under a velocity–time graph, including signed areas.
- Interpret straight, horizontal and curved sections of a velocity–time graph in terms of acceleration.
Kinematics exam tips
Marking Points
- Displacement is the straight-line distance from start to finish in a stated direction.
- Instantaneous speed is the magnitude of velocity at a particular instant.
- Average speed is total distance travelled divided by total time taken.
- Velocity is displacement divided by time and is a vector.
- Acceleration is the rate of change of velocity, so a change of direction also produces acceleration.
- Displacement–time gradient gives velocity.
- Velocity–time gradient gives acceleration.
- Area under a velocity–time graph gives displacement.
- Area under an acceleration–time graph gives velocity change.
- Speed–time graphs give distance from area but do not show direction.
- Displacement–time graphs plot displacement against time.
- The gradient of the graph equals velocity.
- A straight line shows constant velocity and a horizontal line shows zero velocity.
- A tangent to a curve gives instantaneous velocity.
- A negative gradient indicates motion in the negative direction.
- Gradient of a velocity–time graph equals acceleration, calculated as change in velocity divided by change in time.
- A straight line on a velocity–time graph represents constant acceleration; a horizontal line represents zero acceleration.
- Area between the graph line and the time axis represents displacement, found by splitting the region into triangles, rectangles or trapezia.
- Areas below the time axis count as negative displacement, so total displacement is the signed sum of the areas.
- Units must be consistent: velocity in m s⁻¹, time in s, acceleration in m s⁻² and displacement in m.
Examiner Tips
- 💡Write the defining equation and substitute values with units before choosing an option.
- 💡Check whether the quantity is a vector or scalar before comparing magnitudes.
- 💡For round trips, separate total distance from displacement.
- 💡Label axes and units before interpreting any gradient or area.
- 💡Use tangent gradients for curved graphs and count squares for irregular areas.
- 💡State whether an area represents displacement or distance according to the graph type.
- 💡Draw a tangent carefully at the required point for curved graphs.
- 💡Calculate gradient as change in displacement divided by change in time, with units.
- 💡Check the sign of the gradient to state the direction of motion.
- 💡Read the axes and units before calculating; check whether the graph shows velocity or speed, because speed–time graphs do not show direction.
- 💡For area, divide the region into simple shapes and label each area with its sign before adding them.
- 💡For gradient, choose two points on the line that are far apart to reduce reading error, and show the substitution clearly.
Common Mistakes
- Treating distance and displacement as interchangeable: displacement includes direction and can be zero for a closed loop.
- Confusing average speed with instantaneous speed: average speed uses total distance and total time.
- Assuming constant speed means zero acceleration: changing direction at constant speed still gives acceleration.
- Reading area under a displacement–time graph as displacement: area is not used on that graph; gradient gives velocity.
- Using a speed–time graph to find displacement: it gives distance, because direction is lost.
- Ignoring negative regions: area below the time axis counts as negative displacement for velocity–time graphs.
- Reading the height of the graph as velocity: height is displacement; gradient is velocity.
- Using two points to find instantaneous velocity on a curve: a tangent at the point is needed.
- Ignoring the sign of the gradient: a negative gradient means negative velocity, not zero velocity.
- Confusing the roles of gradient and area: the error is treating area as acceleration or gradient as displacement; the correction is that gradient gives acceleration and area gives displacement.
- Ignoring the sign of areas below the time axis: the error is adding all areas as positive; the correction is to subtract areas below the axis when finding total displacement.
- Using the wrong units or mixing them: the error is quoting acceleration in m s⁻¹ or displacement in m s⁻²; the correction is to use m s⁻² for acceleration and m for displacement.
- Assuming a curved velocity–time graph has constant acceleration: the error is reading a curve as a straight line; the correction is that a curve means the gradient, and therefore acceleration, is changing.