Velocity-Time Graph: Uniform Retardation and non-Uniform Acceleration - QS Study
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Velocity-time graph In case of uniform retardation and non-uniform acceleration

Velocity-time graph (In case of uniform retardation): There will always be initial velocity for uniform retardation. In this case also the graph will be a straight line. But its slope will be negative [Figure]. Negative slope means retardation. The slope of the straight line becomes equal to the uniform retardation. Finally the body comes to rest i.e., its velocity becomes zero.

Velocity-time graph (In case of non-uniform acceleration): In case of a body moving with non-uniform acceleration the velocity-time graph becomes a curve [Fig (a) and (b)]. Where velocity increases with time acceleration also increases as shown in Fig. (a) and Fig. (b)].

As before, it can be proved that during time interval (t2 — t1) the average value of acceleration is equal to the slope of the area AB. Instantaneous acceleration at any point in the graph is equal to the slope of the tangent at that point. With passage of time slope continues to increase. It is clear from it that acceleration is not constant [Fig.(c)], rather it increases with time. If the velocity of the body decreases with time or if there is retardation. Acceleration of the point P is obtained from the slope of ∆ADC.

Acceleration = slope = AD/DC.