Representation by graphical methods of uniform and non- uniform…

The idea

Motion graphs represent acceleration by their shape. On a displacement–time graph, the gradient gives velocity: a straight line means uniform velocity, while a curve means changing velocity and therefore acceleration. On a velocity–time graph, the gradient gives acceleration: a straight sloping line means uniform acceleration, a horizontal line means zero acceleration, and a curve means non-uniform acceleration. The area between the velocity–time graph and the time axis gives displacement, with areas below the axis counted as negative. To find a gradient, draw a tangent at the required instant and use Δv/Δt; to find displacement, split the area into triangles, rectangles or trapezia. A velocity–time graph that crosses the time axis shows a change of direction.

What earns the marks

• Interprets the gradient of a displacement–time graph as velocity, including the sign of the gradient.
• Interprets the gradient of a velocity–time graph as acceleration, using a tangent where the graph is curved.
• Recognises that a straight velocity–time line represents uniform acceleration and a curved line represents non-uniform acceleration.
• Finds displacement from the area under a velocity–time graph, treating areas below the time axis as negative.
• Sketches or selects graphs that match a described motion, such as constant velocity followed by uniform deceleration.
• Uses units and scales correctly when reading gradients and areas from axes.

Common mistakes and how to put them right

• Reading the height of a velocity–time graph as displacement.

  Put it right by using the area under the graph for displacement.

• Treating a curved displacement–time graph as constant velocity.

  Put it right by drawing tangents and noting that the gradient changes.

• Ignoring the sign of areas below the time axis.

  Put it right by subtracting those areas when finding displacement.

• Using the whole graph gradient when an instantaneous acceleration is requested.

  Put it right by drawing a tangent at the specified time.

Exam tips

• Label axes with quantity and unit before plotting or interpreting a graph.
• For curved graphs, draw a clear tangent at the required point and show the triangle used for the gradient.
• For area calculations, divide the region into simple shapes and state whether each area is positive or negative.
• Check that the gradient units follow from the axes, for example m s⁻¹ divided by s gives m s⁻².