Answer to Question #230924 in Physics for Samuel

Question #230924

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


1
Expert's answer
2021-08-30T15:05:08-0400

Given:

a=4sinπt/2a=4\sin\pi t/2

x0=0x_0=0

v0=8/πv_0=-8/\pi


The acceleration

a(2)=4sin(π2/2)=0m/s2a(2)=4\sin(\pi*2/2)=0\:\rm m/s^2

The velosity

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

v(2)=8/πcos(π2/2)=8/πv(2)=-8/\pi\cos(\pi *2/2)=8/\pi

The displacement

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

=16/πsinπt/2=-16/\pi\sin\pi t/2

x(2)=16/πsin(π2/2)=0x(2)=-16/\pi\sin(\pi*2/2)=0


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment