Oh man, I had a test today and I didn't know how to do this, it was a bonus mark because we didn't learn it.
How do you show increasing acceleration (not constant) on a distance-time graph?
Is it curve, if so what kind?
2007-12-05 08:31:52 · 4 answers · asked by funkee_fresh721 2 in Science & Mathematics ➔ Physics
oh no!
I had that and then erased it :(
but that does make sense...
thankyou for the answer
2007-12-05 08:39:33 · update #1
Yeah I get it.
Is there any possible way that the curve could be angled downwards (like a sad face) instead of 'happy face' going up?
do you know what I mean by that?
2007-12-05 08:50:39 · update #2
It's a curve. It curves upwards quite steeply. But if it is a distance/time graph it is hard to distinguish it from uniform acceleration, which also curves upwards.
2007-12-05 08:37:55 · answer #1 · answered by za 7 · 0⤊ 2⤋
You can't answer this question in any absolute way without knowing what the shape of the distance-vs-time curve is. If you know that, then you can figure out the change in acceleration curve by taking the derivative.
Here's the general relationship.
Acceleration is the second derivative of distance.
The -change- in acceleration is the derivative of acceleration, or the third derivative of distance.
So, if you have some distance-vs-time curve on a distance-time graph,
1) take the derivative of this curve to get the velocity vs. time
2) take the derivative of the velocity curve to get the acceleration-vs-time curve
3) take the derivative of the acceleration curve to get the change in acceleration vs. time curve,
4) etc.. each derivative gives you the change in the previous curve as a function of time.
Here's an example.
Start with some arbitrary function of position (x) vs time and calculate the derivatives
1) x = t^4 - t^3 + 1
2) dx/dt = velocity = 4t^3 - 3t^2
3) dv/dt = acceleration = 12t^2 - 6t
4) da/dt = change in accel = 24t - 6
5) etc..
Make sense?
BTW, the change in acceleration is often referred to as 'jerk'.
Hope this helps,
-Guru
2007-12-05 08:39:25 · answer #2 · answered by Guru 6 · 0⤊ 0⤋
All I know is straight lines mean no acceleration (constant velocity) and parabolas, or second degree equations (which are ones with an x^2 term in them) represent constant acceleration. I think any other curve that doesn't have a constant for its 2nd derivative would represent a changing acceleration, and the parts of the graph where the second derivative is positive mean increase of the acceleration. A graph that curves upward that is not a parabola?
2007-12-05 08:48:39 · answer #3 · answered by pschroeter 5 · 0⤊ 1⤋
time as x-axis, distance as y-axis...
suppose a car is accelerating on a highway, imagine how it would travel.
At 1 second it would be going really slow
At 2-3 seconds, it would get a little faster
After that it just goes really fast
Obviously, it would be able to travel a greater distance per second because its traveling faster. Get it?
On a graph it would look like a curve that's going upwards.
2007-12-05 08:44:11 · answer #4 · answered by Immatellonu123 4 · 0⤊ 1⤋