The following is a suggested answer for the GCE O Level Physics question in Year 2011 November, Paper 1, multiple choice question 3.
The question provided the speed-time graph of a trolley as the trolley moves across a floor. The student is required to find the distance travelled by the trolley when it travels at constant speed.
The answer for this mutiple choice question is B. That is, the distance travelled is 12 m.
The distance travelled by the trolley is = area under the speed-time graph when the speed is constant
= (4 m/s) x (3 s)
Constant speed means the speed remains the same, unchanged, for a certain period.
From the speed-time graph provided, the trolley is moving at a constant speed from time=4s to time=7s, i.e. over a duration of 3 seconds. The speed of the trolley is 4 m/s during this constant speed period.
Why distance equals area under a Speed-Time Graph?
From the formula :
Speed = Distance travelled/ time
It also means:
Distance travelled= Speed x time
From a Speed-Time graph:
- the y-axis value gives the speed;
- the x-axis value gives the time.
In a Speed-Time graph, area under the graph = (y-axis value) x (x-axis value)
= speed x time
= Distance travelled.