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  4. A particle moves according to the law, x=rcos(π t/2 .) . The distance covered by it the time interval between t= 0 to t=3s is

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Q. A particle moves according to the law, $x=rcos\frac{\pi t}{2 .}$ . The distance covered by it the time interval between t= 0 to t=3s is

NTA AbhyasNTA Abhyas 2022

Solution:

When $t=0, \, x=rcos \frac{\pi \times 0}{2}=r$ ;
When $t=3s, \, x=rcos \frac{\pi \times 3}{2}=0$
Here $\omega =\frac{\pi }{2}$ or $\frac{2 \pi }{T}=\frac{\pi }{2}$ or $T=4s$
$\therefore $ In 3 sec, the particle goes from one extreme to other extreme and then back to mean position. So the distance travelled $=2r+r=3r$