Determine the position functionif the ac- celeration function is a(t) = 3 sin t+1 , the initial velocity is v(0)=0 and the initial position s(0)=4?

Question

1425 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-06T12:13:37

The answer is #=-3sint+1/2t^2+3t#

The acceleration is #a(t)=3sint+1#

The velocity is the integral of the acceleration

#v(t)=-3cost+t+C#

Plugging in the initial conditions

#v(0)=0#

#v(0)=-3cos0+0+C=0#

#=>#, #C=3#

#v(t)=-3cost+t+3#

The position is the integral of the velocity

#s(t)=-3sint+1/2t^2+3t+C#

Plugging in the initial conditions

#s(0)=4#

#s(0)=-3sin0+1/2 0^2+30+C=0#

#=>#, #C=0#

Therefore,

#s(t)=-3sint+1/2t^2+3t#