First slide

Graphical representation-Motion in 1 d

Question

From the velocity-time graph, given in figure of a particle moving in a straight line, one can conclude that

Moderate

A

Its average velocity during the 12 s interval is 24/7 ms^-1.
B

Its velocity for the first 3 s is uniform and is equal to 4 ms^-1.
C

The body has a constant acceleration between t = 3 s and t = 8s.
D

The body has a uniform retardation from t = 8 s to t = 12 s.

Solution

$Displacement in 12 s = Area under v - t graph$
$= \frac{1}{2} \times (12 + 5) 4 = 34 m$
$V_{av} = \frac{Displacement}{Time} = \frac{34}{12} = \frac{17}{6} {ms}^{- 1}$
Hence, (a) is incorrect; (b) is incorrect because during first 3 s, velocity increases from 0 to 4 ms^-1 option; (c) is incorrect, because in part AB velocity is constant.

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