Question

A particle moves along a straight line with an acceleration of a=4sinπt/2 m/s^2. If the displacement at t=0 is 0 and the initial velocity is -8/π m/s. find the acceleration after 2seconds and velocity after 2 seconds and displacement after 2seconds

Answer 1

Given:

$a=4\sin\pi t/2$

$x_0=0$

$v_0=-8/\pi$

The acceleration

$$a(2)=4\sin(\pi*2/2)=0\:\rm m/s^2$$

The velosity

$$v(t)=\int a(t)dt=\int 4\sin\pi t/2dt \\=-8/\pi\cos\pi t/2+C,\quad C=0$$

$$v(2)=-8/\pi\cos(\pi *2/2)=8/\pi$$

The displacement

$$x(t)=\int v(t)dt=\int (-8/\pi\cos\pi t/2)dt$$

$$=-16/\pi\sin\pi t/2$$

$$x(2)=-16/\pi\sin(\pi*2/2)=0$$