How Do You Calculate Velocity from an Acceleration-Time Curve?

[Audaciter]

1. We are given a simple acceleration vs time curve. It shows that the object has a constant acceleration of 5 m/s2 for 10 seconds, and then from 10 to 26 seconds has a constant acceleration of 15 m/s2. The question asks me to give an equation for velocity as a function time using only the variable T.



2. V = V initial + a*t
?



3. This is a multi part question, and I have gotten the first part correct. The first part simply asks for the equation from 0 < t <10. I responded that v = 5*t , and got it correct. A similar question within the same problem asks, "what if the initial velocity is 35 m/s" I responded v = 35 + 5*t and got it correct.

The next part is to give an equation (using the same variables) but for 10 < t < 26. I have tried v= v initial +at to no avail.

The real problem is, because this is online homework, I can't tell if I am doing it wrong, or typing it wrong. I've looked through the book and my notes, and have not seen anything to help me in the right direction.

So what I am doing wrong for the 10 < t < 26 portion?

Thanks to all.

 

[SammyS]

... "what if the initial velocity is 35 m/s" I responded v = 35 + 5*t and got it correct.

The next part is to give an equation (using the same variables) but for 10 < t < 26. I have tried v= v initial +at to no avail.[/b]
...

So what I am doing wrong for the 10 < t < 26 portion?

Thanks to all.

What does v_initial correspond to for this part. It might be better to call it v₁₀.

When 10 < t < 26, for what amount of time has the object has been accelerating at 15m/s²?

 

[Audaciter]

Thank you for the quick reply.

I would assume that V inital for 10 < t 26 is simply 5*t, from the first portion of the question, is that correct? Meaning v = 5*t + 15t.

The object instantaneously accelerates from 5 m/s2 to 15 at t = 10. The graph looks like a single step if you know what I mean.

It has the same basic shape as this graph, but mine is a "step up" rather than a "step down" with different numbers obviously.

[PLAIN]http://img268.imageshack.us/img268/8762/acvt9nz.jpg

 

[gneill]

1. We are given a simple acceleration vs time curve. It shows that the object has a constant acceleration of 5 m/s2 for 10 seconds, and then from 10 to 26 seconds has a constant acceleration of 15 m/s2. The question asks me to give an equation for velocity as a function time using only the variable T.

It sounds like you're going to need to employ the unit step function in your expression.

edit: Unless of course you only need to express the time interval from 10 to 26 seconds. Does the problem text make it clear whether or not the initial 35m/s velocity mentioned elsewhere is to be assumed in this section too?

 

[Audaciter]

Sorry, I didn't make it clear. There are 2 questions dealing with the same graph, and each of those has two parts.

Question 1 assumes a initial velocity at t = 0 is v = 0.
Then 1a) asks for what I discussed above. Equation for velocity as a function of time for t <10. 1b) asks for the function for 10 < t < 26.

Question 2 then assumes an initial velocity at t = 0 is v = 35; 2a and 2b are the same as question 1.

So, if you are only doing the time interval for 10 < t < 26 (with either question) do you use the initial velocity of THAT segment of the motion, or the initial velocity of the entire motion?

I guess my root problem is I don't know how to get an equation for the second time interval. I have correctly gotten the equation for 1a and 2a, but can't seem to get 1b and 2b...I hope I am not confusing this more.

Thank you.

 

[gneill]

If you only need to produce an equation for a specific time interval, then I'd use the velocity at the beginning of the interval as the initial velocity and forget the past.