# Difference between position time, velocity time and acceleration time graph

1. Sep 14, 2011

### h2chawwaa

What is the difference between position time graph, velocity time graph and acceleration time graph and how would each of them look like when drawn?

2. Sep 14, 2011

### easwaran.sr

exponential, ramp,straight line parallel to time axis

3. Sep 14, 2011

### gsal

Change of position per unit time is motion and hence, there is velocity there...for as long as velocity is the rate of change of position vs time, we can say that velocity is the derivative of position vs time curve.

Acceleration is the rate of change of velocity per unit time...and so, acceleration is the derivative of the velocity vs time curve.

So, if something is not moving, and it has the same position at all times (horizontal line in y vs t plot), vel=0, acc=0

If something is moving at a constant rate, the plot is an inclined line..its derivative is a constant (slope) which is the speed. The derivative of a constant (speed) is zero (acc=0).

If something is moving at various speeds/acceleration, the position plot will be all over the place, the velocity will be the derivative of such curve, and acceleration that derivative of the speed curve.

4. Sep 15, 2011

### daveb

There are also relationships when integrating velocity as a function of time and acceleration as a function of time.

5. Sep 15, 2011

### 256bits

If the object is moving at constant acceleration then the plot of position versus time is exponential, a plot of velocity vs time is a ramp ( ie sloped ), and the plot of acceleration vs time is a horizontal straight line.

If the object is moving at a constant velocity then the plots become a ramp, a horizontal line, and a horizontal line with acceleration = 0.

If the object has no velocity nor acceleration then the plot of position is a horizontal staright line and the plots of both velocity and acceleration are horizontal straight lines with velocity=0 and acceleration=0.

6. Sep 15, 2011

### rcgldr

It would be quadratic, x(t) = x0 + v0 t + 1/2 a t2.

7. Sep 15, 2011

### Trevormbarker

the derivative of an exponential is another expenetial which is clearly not what happens when you differentiate the d-t graph of a uniformally accelerated object, it has to be quadratic, which leads to a linear v-t graph when differentiated and then when differentiated the second time to a horrizontal line