With the help of a simple case of an object moving with a constant velocity show that the area under velocity – time curve represents distance covered over a given time interval.
Answers
Answer:
The area under a velocity-time graph is a representation of the displacement. If the area is over a time interval, then the displacement during that time interval can be measured by the area under the graph bounded by the time interval. ... Bonus: the slope of a V-t graph is a measure of acceleration.
Therefore the area under velocity – time curve represents the distance covered over a given time interval.
Given:
An object is moving with a constant velocity.
To Find:
The area under velocity – time curve represents the distance covered over a given time interval.
Solution:
The given question can be easily solved using the approach shown below.
We know the formula for velocity,
⇒ Velocity = ( Distance Travelled ) / ( Time Taken )
Then, Distance traveled = Velocity × Time Taken
A graph is plotted for Velocity on Y-axis and Time Taken on X-axis as shown in the figure attached.
The graph will be a horizontal line as the velocity is uniform.
So Area under the curve will be equal to the area of the rectangle.
On the Y-axis length of the rectangle = velocity V
On the X-axis length of the rectangle = Time interval ( t₂ - t₁ ) = Time Taken T
So Area of the rectangle = Velocity × Time Taken
⇒ But from the formula of velocity, Velocity ×Time Taken = Distance traveled
Therefore the area under velocity – time curve represents the distance covered over a given time interval.
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