A body oscillates with SHM according to the equation in (SI units) x=5 cos [2 π t+(π/4)] At t=1.5 s, the speed and acceleration of the body are:

Question

A body oscillates with SHM according to the equation in (SI units) x=5 cos [2 π t+(π/4)] 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

Tardigrade Admin · Accepted Answer

v=(d x/d t)=(-5)(2 π) sin (2 π t+(π/4)) At t=1.5 s v=-10 π sin (3 π+(π/4))=22 ms -1 a=(d v/d t)=-(5)(2 π)2 cos (2 π t+π / 4) At t=1.5 s , a=(-5)(2 π)2 cos (3 π+(π/4))=140 ms -2

Q. A body oscillates with $S H M$ according to the equation in (SI units) $x = 5 cos [2 π t + \frac{π}{4}]$ At $t = 1.5 s$ , the speed and acceleration of the body are:

$11 m s^{- 1}$ and $70 m s^{- 2}$

$22 m s^{- 1}$ and $140 m s^{- 2}$

$11 m s^{- 1}$ and $140 m s^{- 2}$

$22 m s^{- 1}$ and $70 m s^{- 2}$

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

Q. A body oscillates with SHM according to the equation in (SI units) x=5cos[2πt+4π​] At t=1.5s, the speed and acceleration of the body are:

11ms−1 and 70ms−2

22ms−1 and 140ms−2

11ms−1 and 140ms−2

22ms−1 and 70ms−2