# Relation between acceleration and time

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1. Jun 17, 2015

I have a problem. As I was finding the torque for an engine. I have. I get a question about the relation of acceleration and time.
How will be the graph of varying acceleration and time if acceleration decreases?
Will it be a straight line with negative slope or any other shape?

2. Jun 17, 2015

### Staff: Mentor

This is impossible to tell without more information. It's like asking "here is a car, what will its speed be over time?"

3. Jun 17, 2015

### RUber

If you are plotting acceleration on the y axis and time on the x axis, then a horizontal line would indicate constant acceleration. Negative slope indicates decreasing acceleration, and positive slope indicates increasing acceleration.
The question is, how is your acceleration changing? Do you have a formula for it?

4. Jun 17, 2015

### insightful

Most cars (including drag racers) have maximum acceleration near t=0. Then acceleration declines rather quickly before curving to a more gentle downward slope. You'll need data and curve-fitting techniques to find the formula for your application.

5. Jun 18, 2015

### Staff: Mentor

Not if they are parking somewhere (a=0), or moving in traffic jams or whatever. That's the point, we have no idea what happens so it is impossible to know the acceleration.

6. Jun 18, 2015

Thank you for such a response to my first question to Physics forum.

7. Jun 18, 2015

Hello
Today I get the graph of acceleration and time for my engine.
It will have a shape of paarabola x=-y^2 in first qudrent from Max acceleration to a=0.

Now I have a question regarding the reletion of power and acceleration & relation of torque and acceleration.
How to get relation for my engine. having max torque 18.6 N-m @2800 rpm.
how can I accelertion from power.

8. Jun 18, 2015

### RUber

This web page spells it out pretty simply. http://theory.uwinnipeg.ca/physics/rot/node5.html
If you know torque, $\tau$, mass, m, and you know the radius of the thing you are rotating, $r$, you can relate torque to acceleration by:
$\tau = m r a$

9. Jun 18, 2015

### insightful

I assume you mean to end up with an equation like:

a = a0 - C*sqrt(t)

For example, if initial acceleration were 1 m/s2 and acceleration drops to 0 after 20 seconds, you have:

a = 1 - 0.2236*sqrt(t)

Now, if you know the torque from the engine at a point in time, you can calculate the acceleration by calculating the force the wheels are applying to the vehicle, using F = ma. In practice, this is not possible because engine torque is not known at every point in time.

(Are we talking about a vehicle, like a motorbike?)

10. Jun 18, 2015

Thank you for response...

But what is the C here?
How did you get the value of C=02236 here?

I am making an ATV car.

11. Jun 18, 2015

### insightful

C is a constant in the equation. It is found by putting my assumption in the example I gave that a=0 at t =20 s:

0 = 1 - C*sqrt(20) and solve for C.