The correct distance-time graph is A
Explanation:
There is the following relationship between distance-time, speed-time and acceleration-time graphs for an object in motion:
- The gradient of a distance-time graph is the speed
- The gradient of a speed-time graph is the acceleration
- The area under a speed-time graph is the distance covered
- The area under an acceleration-time graph is the speed
In this problem, we are given the speed-time graph of the object. We notice that it is a straight line with positive slope: so, this means that the speed is increasing at a constant rate, therefore the object has a constant acceleration.
This means that the speed is increasing linearly:
[tex]speed=at[/tex]
(where a is the acceleration and t is the time)
And therefore, the distance covered is the area under the graph, which therefore has a form
[tex]distance=\frac{1}{2}at^2[/tex]
so, it is proportional to [tex]t^2[/tex]: therefore, the correct distance-time graph is the first one, A.
Learn more about speed and distance:
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