The velocity - times graph for a uniformly retarded body is a straight line inclined to the time axis with an obtuse angle. How is retardation calculated from the velocity

Foundation

Physics Foundation

Vertical Motion

Question

The velocity - times graph for a uniformly retarded body is a straight line inclined to the time axis with an obtuse angle. How is retardation calculated from the velocity - time graph ?

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The retardation is nothing but the negative acceleration. For acceleration, we find the slope of the velocity - time graph. Similarly, in order to calculate the retardation from the velocity - time graph, a negative slope should be obtained. The graph makes an obtuse angle θ with the time axis.

The slope can be obtained by marking two points on the graph and finding the corresponding values of velocity v₁, v₂ and time t₁, t₂.

Then the retardation can be found by the relation :

a = \frac{Δv}{Δt} = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}

This quantity a will be negative because v₁ > v₂.

Alternatively, the retardation a = tan θ = negative because θ > 90°.

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