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Q.

A body covers 100cm in first 2 seconds and 128cm in the next two seconds moving with constant acceleration. Find the average velocity of the body between t = 3s and t = 5s

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a

7 cm/s

b

43cms⁻¹

c

71cms⁻¹

d

Zero

answer is C.

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Detailed Solution

$\begin{array}{l} 100 = 2 u + \frac{1}{2} a \times 2^{2} \\ u + a = 50 \dots \dots . (1) \\ \begin{array}{l} 228 = 4 u + 8 a \\ u + 2 a = 57 \dots \dots (2) \end{array} \end{array}$

$solving u = 43 {cms}^{- 1} a = 7 {cms}^{- 2}$

$\begin{array}{l} V_{avg} = \frac{u (t_{2} - t_{1}) + \frac{1}{2} a (t_{2}^{2} - t_{1}^{2})}{t_{2} - t_{1}} \\ = u + \frac{1}{2} a (t_{1} + t_{2}) \\ = 43 + \frac{1}{2} \times 7 (8) {cms}^{- 1} = 71 {cms}^{- 1} \end{array}$

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