Question

A body oscillates with SHM according to the equation $x=5.0cos\left(2\pi t+\pi \right)$. At time $t=1.5s$, its displacement, speed and acceleration respectively is:

• A. $0,-10\pi ,+20{\pi }^2$
• B. $5,0,-20{\pi }^2$
• C. $2.5,+20\pi ,0$
• D. $-5.0,+5\pi ,-10{\pi }^2$

Answer 1

The correct option is B $5,0,-20{\pi }^2$

Given,

$x=5cos(2\pi t+\pi )$

$t=1.5sec$

Displacement, $x=5cos(2\pi \times 1.5+\pi )=5cos\left(4\pi \right)$

$x=5m$. . . . . .(1)

Velocity, $v=\frac{dx}{dt}$

$v=-10\pi sin(2\pi t+\pi )$

$v=-10\pi sin(2\pi \times 1.5+\pi )$

$v=-10\pi sin\left(4\pi \right)$

$v=0m/s$. . . . .(2)

Acceleration, $a=\frac{dv}{dt}$

$a=-20{\pi }^{2}cos(2\pi t+\pi )$

$a=-20{\pi }^{2}cos(2\pi \times 1.5+\pi )$

$a=-20{\pi }^{2}cos\left(4\pi \right)$

$a=-20{\pi }^2$

The correct option is B.