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You can calculate the tangent for a give time, T, as follows:
Substitute the value of the time in the distance-time equation to find the distance at the given time. Suppose it is f(T).
Differentiate the distance-time equation with respect to time. For any given time, substitute its value in the derivative and evaluate. That is the gradient of the tangent, v.
Then equation of the tangent is
f(T) - f(t) = v*(T - t)
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What does a tangent to a velocity-time graph measure?
A tangent to a velocity-time graph represents the instantaneous acceleration of an object at that specific moment in time. It shows how the velocity is changing at that particular point.
Calculate distance from a velocity time graph?
To calculate distance from a velocity-time graph, you would find the area under the curve, as this represents the displacement or distance traveled. If the graph is above the time axis, calculate the area above the time axis, and if it dips below, calculate the area below the time axis. Summing these two areas will give you the total distance traveled.
How do you find instantaneous velocity from position time graph?
To find instantaneous velocity from a position-time graph, you calculate the slope of the tangent line at a specific point on the graph. The slope represents the rate of change of position at that instant, which is equivalent to the velocity at that particular moment.
What does the slope of distance versus time graph represent physically?
The slope of a distance versus time graph represents the speed or velocity of an object. A steeper slope indicates a higher speed, while a gentler slope indicates a slower speed. If the slope is negative, it means the object is moving in the opposite direction.
When do two different distance-time graphs have matching velocity-time graphs?
Two different distance-time graphs have matching velocity-time graphs when the slope of the distance-time graph represents the velocity in the velocity-time graph, as velocity is the derivative of distance with respect to time. This means that the steeper the distance-time graph, the greater the velocity on the velocity-time graph at that point.
