Aparticle travels along the x-axis in such a way that its acceleration at time t is a(t) = 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 = 5. (round your answers to two decimal places.)

The acceleration of the particle as a function of time t is

The velocity of the particle at time t is the integral of the acceleration:

where the constant C can be found by requiring that the velocity at time t=0 is v=3:

and we find 
so the velocity is


The position of the particle at time t is the integral of the velocity:

where D can be found by requiring that the initial position at time t=0 is zero:
x(0)=0
from which we find D=0, so 
  

To solve the problem, now we just have to substitute t=5 into x(t) and v(t) to find the position and the velocity of the particle at t=5.

The position is:

and the velocity is:

If football was tossed in air without gravity or friction the ball would go into space