Finding Initial Velocity v0x for Particle with Non-Constant Acceleration

[klapklap___]

Homework Statement

Find the initial velocity v0x such that the particle will have the same x-coordinate at time t= 4.07 s as it had at t=0.

The acceleration of a particle is given by ax(t)=−2.00 m/s2 +( 3.09 m/s3 )t.

Homework Equations

v = v0 + a t
Δx = ((v+v0)/2)t
Δx = v0t + 1/2at^2
v^2 = v0^2 +2aΔx

a = constant acceleration, t = time, Δx = change in x, v0x = initial velocity

The Attempt at a Solution

I figure this question is about being able to use the kinematic equations; putting known values in and solving for unknown values with the specific choice of the equation which is most relevant with given data, however the kinematic equations I have don't specify what the acceleration equation means in the question. Maybe it does, but I can't figure out what is what and where. I also googled profusely and couldn't find an equation for ax(t) where the variables are present so that I could find how the kinematic equations and the ax(t) equation are related.

So really I just need to know how the two are related so that I can make sense of what given data I already have. Thanks.

 

[kuruman]

The instantaneous velocity is not v = v₀ + at when the acceleration depends on time. You need to find the correct expression for v(t). You will be better off if you use your brain instead of google. Hint: v(t) = ∫a(t) dt

 

[Chandra Prayaga]

You are trying to use the wrong set of "relevant" equations. As kuruman points out in post #2, your acceleration is not constant. You must read your textbook to find out how you can get velocity and position if the acceleration is not constant. It is not a good idea to do problems without reading the relevant portion from the textbook.