First slide

Rectilinear Motion

Question

A body travels 200 cm in the first 2 s and 220 cm in the next 4 s with deceleration. The velocity of the body at the end of the seventh second is

Moderate

A

5 ${cms}^{- 1}$
B

10 ${cms}^{- 1}$
C

15 ${cms}^{- 1}$
D

20 ${cms}^{- 1}$

Solution

$\begin{array}{l} 200 = u \times 2 - (1 / 2) a (2)^{2} \\ or u - a = 100 . . . . (i) \\ 200 + 220 = u (2 + 4) - (1 / 2) (2 + 4)^{2} a \\ or u - 3 a = 70 . . . . (i i) \end{array}$
$Solving Eqs (i) and (ii), we get a = 15 {cms}^{- 2} and u = 115 {cms}^{- 1} .$
$Further, v = u - a t = 115 - 15 \times 7 = 10 {cms}^{- 1}$

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