Question

1) A 2.0 kg particle moves as a function of time as follows:

             x = 3.5 sin (1.5t+π/2)

Where, distance is measured in meters and time in seconds.

(a) What is the equation of the velocity and the acceleration of this particle?

Answer 1

$v=\frac{dx}{dt}=3.5\cdot\cos(1.5t+\pi/2)\cdot1.5=5.25\cdot\cos(1.5t+\pi/2)$

$a=\frac{dv}{dt}=-5.25\cdot\sin(1.5t+\pi/2)\cdot1.5=-7.875\cdot\sin(1.5t+\pi/2)$