Question

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

• A. r
• B. 2r
• C. 3r
• D. 4r

Answer 1

Answer: (C)

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 $=2r+r=3r$