Area under a velocity-time graph gives distance travelled
4 marks · EasyA ball rolls down a ramp, starting from rest. The velocity–time graph for the first 4 seconds is a straight line from (0, 0) to (4, 8).
Draw the velocity–time graph for this motion, labelling both axes with appropriate units.
Explain how you would use the area under the graph to find the distance travelled in these 4 seconds.
Calculate the distance the ball rolls in the 4 seconds.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) Straight line from (0,0) to (4,8), axes labelled (time s, velocity m/s) · must show Correct straight line, Axes labelled
(b) The area (a triangle) under the graph equals the distance the ball travels. · must show Mentions area under graph, States it gives distance
(c) 16 m · must show Area using 0.5×4×8 or correct method
Must show: Graph drawn, Axes labelled (time in s, velocity in m/s), Triangle area calculated
Common mistakes: Calculation as rectangle not triangle
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Graph: correct straight line from (0,0) to (4,8); axes labelled.
B1 (b) · 1 mark · Mentions area under graph gives distance.
M1 (c) · 1 mark · Uses correct area formula for triangle.
A1 (c) · 1 mark · Distance correctly calculated as 16 m.
Worked solution
a) Draw a graph with time on the x-axis (0–4 s) and velocity on the y-axis (0–8 m/s). Draw a straight line from (0,0) to (4,8).
b) The area under the graph (a triangle) gives the distance the ball travels.