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In a velocity–time graph, the graph is a straight horizontal line at 10 m/s for 5 seconds. Then the distance travelled is ____________.
2 m
50 m
10 m
5 m
50 m
Since the velocity is constant, the distance is simply the area of the rectangle formed by the velocity-time graph, which is the product of the height (10) and the base (5).
Velocity (v) = 10 m/s, Time (t) = 5 seconds
Distance=Velocity×Time
Since the velocity is constant, the distance is simply the area of the rectangle formed by the velocity-time graph, which is the product of the height (10) and the base (5).
Students often mistake a horizontal velocity-time graph for a stationary object (v=0), but here the constant height 10 indicates the object is moving at a uniform speed.
Identify given parameters
Extract the constant velocity (v=10 m/s) and the duration of travel (t=5 s) from the problem statement.
v=10,t=5
Apply distance formula
In a velocity-time graph, the distance travelled is equal to the area under the curve. For a horizontal line, this is the area of a rectangle given by the product of v and t.
Distance=v×t
Calculate the result
Substitute the given values into the equation: Distance=10 m/s×5 s.
Distance=50 m
B is correct because the product of the constant velocity of 10 m/s and the time interval of 5 seconds yields 50 m.
This concept of 'Area under the curve' is a fundamental precursor to Calculus, where the integral of velocity with respect to time gives displacement.
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