The velocity-time graph of a train traveling between two stations is plotted below.
a) Find the acceleration of the train at t = 3 s.
b) Find the displacement of the train after 12 seconds.

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Solution

a) $T h e s l o p e o f v e l o c i t y - t i m e g r a p h g i v e s a c c e l e r a t i o n$
$S l o p e = (y_{2} - y_{1}) / (x_{2} - x_{1})$
$S l o p e = (6 - 0) / (3 - 0)$
$= 2 m / s^{2}$
$S o t h e a c c e l e r a t i o n o f t h e t r a i n a t t = 3 i s 2 m / s^{2} .$
[1 Marks]
b) Displacement of the train after 12 s = area under v-t curve till l2 s.
$D i s p l a c e m e n t = A r e a = ½ \times 6 \times 12 + 12 \times 6$
$= 36 + 72$
$= 108 m$
[2 Marks]

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