A particle moves according to the law x = a $\cos \frac{πt}{2}$ . The distance covered by it in the time interval between t = 0 to t = 3 sec is

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3 a

4 a

2 a

answer is B.

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Detailed Solution

$\begin{array}{l} x = acos (\frac{πt}{2}) = acos ωt \\ ω = \frac{π}{2}; \frac{2 π}{T} = \frac{π}{2} T = 4 sec \\ 0 to 1 \sec \to a; 1 to 2 \sec \to a \\ 2 to 3 \sec \to a; so, total distance = 3 a \end{array}$

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