Question

A body oscillates with $SHM$ according to the equation in (SI units) $x=5 \cos \left[2 \pi t+\frac{\pi}{4}\right]$ At $t=1.5 \,s$, the speed and acceleration of the body are:

• A. $11 \,ms ^{-1}$ and $70\, ms ^{-2}$
• B. $22\, ms ^{-1}$ and $140 \,ms ^{-2}$
• C. $11 \,ms ^{-1}$ and $140\, ms ^{-2}$
• D. $22 \,ms ^{-1}$ and $70 \,ms ^{-2}$

Answer 1

Answer: (B)

$ v=\frac{d x}{d t}=(-5)(2 \pi) \sin \left(2 \pi t+\frac{\pi}{4}\right)$
At $t=1.5 \,s$
$v=-10 \pi \sin \left(3 \pi+\frac{\pi}{4}\right)=22\, ms ^{-1}$
$a=\frac{d v}{d t}=-(5)(2 \pi)^{2} \cos (2 \pi t+\pi / 4)$
At $t=1.5\, s , a=(-5)(2 \pi)^{2} \cos \left(3 \pi+\frac{\pi}{4}\right)=140 \,\,ms ^{-2}$