Finding Initial Velocity v0x for Particle with Non-Constant Acceleration

In summary, the question is asking for the initial velocity v0x of a particle at time t=0, such that it will have the same x-coordinate at t=4.07s. The acceleration of the particle is given by ax(t)=−2.00 m/s2 +( 3.09 m/s3 )t. To solve this problem, one must use the kinematic equations, specifically v(t) = ∫a(t) dt, to find the velocity and position of the particle when the acceleration is not constant. It is important to refer to the textbook for the relevant information and not rely solely on internet sources.
  • #1
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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.
 
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  • #2
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
 
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  • #3
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.
 
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Related to Finding Initial Velocity v0x for Particle with Non-Constant Acceleration

1. What is the formula for calculating initial velocity (v0x)?

The formula for calculating initial velocity (v0x) is v0x = (xf - xi)/t, where v0x is the initial velocity, xf is the final position, xi is the initial position, and t is the time.

2. How is initial velocity (v0x) related to acceleration?

Initial velocity (v0x) is related to acceleration through the equation a = (v0x - v)/t, where a is the acceleration, v0x is the initial velocity, v is the final velocity, and t is the time.

3. What is the difference between initial velocity (v0x) and final velocity (v)?

Initial velocity (v0x) is the velocity at the beginning of an object's motion, while final velocity (v) is the velocity at the end of an object's motion.

4. What units are used for initial velocity (v0x)?

The units for initial velocity (v0x) depend on the units used for distance and time in the formula. For example, if distance is measured in meters and time is measured in seconds, then initial velocity would be in meters per second (m/s).

5. Can initial velocity (v0x) be negative?

Yes, initial velocity (v0x) can be negative. A negative initial velocity indicates that the object is moving in the negative direction (opposite to the positive direction) at the beginning of its motion.

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