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:
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: