Antidifferention?

Question

A particle travels along the x-axis in such a way that its acceleration at time t is a(t)=(sqrt(t))+t² If it starts at the origin with an initial velocity of 3 that is s(0)=0 and v(0)=3  determine its position and velocity when t=3 

 

1.) s(3)=

2.) v(3)=

 

Answer 1

dv = (x^½ + t²)dt

 

v = [(2/3)t^(3/2) + (1/3)t³ + 3)]  where the constant 3 is v(0).

 

ds =  [(2/3)t(^3/2) + (1/3)t³ + 3)] dt

 

s = (4/15)t^5/2 + (1/12)t⁴ + 3t + s(0) and the last term is zero.