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Distance - Time Graph

The a-t graph...

Question

The a-t graph of particle moving along a straight line is given below. At t=0s its velocity is V and its velocity at t=4s is 3V then what is its velocity at t=6s?
(1) 5 m/s
(2) 15 m/s
(3) 20 m/s
(4) 25 m/s

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Solution

$T h e a r e a u n d e r a - t g r a p h g i v e s c h a n g e i n v e l o c i t y T h e a r e u n d e r t h e a - t g r a p h i s i n t h e f o r m o f t r a p a z e u m w i t h p a r a l l e l s i d e s 6 a n d 2 r e s p e c t i v e l y; a n d h e i g h t b e i n g 5 A r e a u n d e r a - t g r a p h = \frac{1}{2} (6 + 2) \times 5 \Rightarrow ∆ v = \frac{1}{2} (6 + 2) \times 5 = 20 m / s v_{f} - v_{i} = 20 m / s G i v e n : v_{i} = 0 v_{f} = 20 m / s$

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