Movement and Position
5 marks · NormalA car starts at rest, accelerates uniformly to a speed of 20 m/s in 4 seconds, then travels at constant speed for 6 seconds.
Draw a labelled velocity–time graph for the motion of the car from 0 to 10 seconds.
Calculate the acceleration during the first 4 seconds.
Calculate the total distance travelled in the 10 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) Graph with time (0–10 s), velocity (0–20 m/s), straight line rising from (0,0) to (4,20), then horizontal from (4,20) to (10,20). · must show Axes labelled, correct plot of acceleration and constant speed
(b) 5 m/s² · must show Correct use of acceleration formula
(c) 120 m. (Triangle area: 0.5×4×20=40 m; Rectangle area: 6×20=120 m; Total = 40+120=160 m) m · must show Working and correct total
Also accept: Accept correct plot and alternative calculation methods
Common mistakes: Mixing up time intervals; Not separating acceleration and constant speed regions
Show mark scheme and worked solution
Marking points
B1 (a) · 2 marks · Graph correctly labelled; shape matches description with correct time and velocity points.
M1 (b) · 1 mark · Acceleration calculated: (20-0)/4=5 m/s².
M2 (c) · 1 mark · Finds area under graph in two parts: triangle + rectangle.
A1 (c) · 1 mark · Adds triangle and rectangle areas for total distance: 40 + 120 = 160 m. (follow-through)
Worked solution
a) Velocity–time graph: time on x-axis, velocity on y-axis. From 0 to 4 s, line rises from 0 to 20 m/s; from 4 to 10 s, horizontal at 20 m/s.