A particle is moving with acceleration a(t)=2-3t we know that t=0: v(0)=-1 and s(0)=1 determine s(2)

Question

A particle is moving with acceleration a(t)=2-3t we know that t=0: v(0)=-1 and s(0)=1 determine s(2)

Answer 1

Just integrate and substitute for initial values:

s(t) = t² - (1/2)t³ - t +1

Then calculate s(2).

What do you not understand?

The integral of acceleration is velocity.

Integrate the equation for acceleration to get velocity and use v(0) to evaluate the constant of integration.

The integral of velocity is distance.

Integrate v(t) determined above and use s(0) to evaluate the constant of integration.

Then evaluate s(2).