Distance-time graphs
3 marks · HardA car is moving at a constant speed. The driver sees a red traffic light 120 m ahead and applies the brakes after 3 seconds. The car slows down uniformly and stops 10 seconds later, right at the light.
Sketch a distance–time graph for the entire journey from the point where the driver sees the red light until the car stops (from 0 to 13 seconds). Label the axes and mark clearly when the car starts braking.
State and explain how the slope of the graph changes during the braking period.
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) Graph: straight line for the first 3 seconds, then a curve that gets less steep and levels out at 120 m at 13 seconds; axes labelled; braking point marked at 3 s. · must show Axes labelled distance (m), time (s), Straight line for 0-3 s, Curve for 3-13 s flattening at 120 m, Braking point marked
(b) The slope decreases during braking, showing the speed reduces until it becomes zero when the car stops. · must show Slope decreases, Represents slowing down, Zero slope when stopped
Common mistakes: Not showing a curve during braking; Incorrect axes labels
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Correctly sketches axes (distance and time) and marks braking at 3 s
B2 (a) · 1 mark · Shows a straight line (constant gradient) for 0–3 s and a decreasing gradient (curve) for 3–13 s, flattening at 120 m
B3 (b) · 1 mark · Explains slope (gradient) decreases during braking, representing decreasing speed, reaching zero at stop
Worked solution
(a) Draw axes (horizontal: time in seconds; vertical: distance in metres). From 0–3 s, draw a straight rising line. From 3–13 s, draw a curve that becomes less steep, flattening at 120 m at 13 s. Mark 'brakes applied' at 3 s.
(b) The slope of the distance-time graph decreases during braking: this shows the speed reduces. When the car stops, the graph becomes flat (zero slope).