First slide

Periodic Motion

Question

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

Easy

A

2 a
B

3a
C

4 a
D

a

Solution

$\large x\, = \,a\cos \left( {\frac{\pi }{2}} \right)\, = \,a\cos \omega t$
$\large \omega \, = \,\frac{\pi }{2};\,\frac{{2\pi }}{T}\, = \,\frac{\pi }{2}\,\,\,\,\,\,\,\,\,\,\,T\, = \,4\sec$
0 to 1 sec $\large \to$ a ; 1 to 2 sec $\large \to$ a
2 to 3 sec $\large \to$ a ; so, total distance = 3a

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