Question

Figure below shows a velocity-time graph for a car starting from rest. The graph has three parts AB, BC and CD.
a) Is the magnitude of acceleration higher or lower than that of retardation? Give a reason.
b) Compare the magnitude of acceleration and retardation.

Answer 1

(a) We know, the slope of velocity-time graph represent acceleration. Here AB shows motion with uniform acceleration and CD shows motion with uniform retardation. Slope of line AB is less in comparison to the line CD. Hence the magnitude of acceleration is lower than that of retardation.
(b) Acceleration in part AB:
$\text{Acceleration}{a}_{AB}=\frac{\text{change in velocity}}{\text{time taken}}=\frac{v_0-0}{t-0}=\frac{v_0}{t}$

Magnitude of acceleration $a_{AB}=\frac{v_0}{t}$
Acceleration in part CD:
$\text{Acceleration}{a}_{CD}=\frac{\text{change in velocity}}{\text{time taken}}=\frac{0-v_0}{2.5t-2t}=\frac{-2v_0}{t}$

Magnitude of retardation $a_{CD}=\frac{2v_0}{t}$
Hence, $\frac{a_{AB}}{a_{CD}}=\frac{1}{2}$
The magnitude of acceleration and the magnitude retardation are in the ratio $1:2$.