Finding an Equation through Integrals

[AxeluteZero]

Position Function from Constant Acceleration Equation

Homework Statement

The acceleration of a certain rocket is given by a_x = bt, where b is a positive constant.

(a) Find the position function x(t) if x = x0 and v0 at t = 0. (Use x_0 for x0, v_0 for v0, b, and t as necessary.)
x(t) =

Homework Equations

(Hint given): The velocity function is the time integral of the acceleration function. The position function is the time integral of the velocity function. The two integration constants can be determined by applying the given initial conditions when the time is equal to zero.

$$\Delta$$s = v_i($$\Delta$$) + (1/2)a($$\Delta$$)²

The Attempt at a Solution

a_x = bt

so a = bt

v = int (a dt) = b * int (t dt) = b (.5t²)

x = b/2 int (t²) dt

Is my thinking in the right spot? I don't know if I'm not integrating correctly or if I need to plug the integrations into an equation...?

 

[ehild]

You have to include a constant C when integrating. So v=0.5*b*t²+C.

If the initial velocity is v₀, C=v₀.

Now integrate v(t), do not forget the integration constant again.

ehild