# Example of x0 in the kinematic equation for displacement

1. May 2, 2013

### e-zero

In the kinematic equation x = x0 + v0 * t + .5 * a * t^2, can someone give me an example in which x0 has a value that is not zero?

2. May 2, 2013

### WannabeNewton

Hi e-zero! $x_{0}$ is just the initial position of the test particle that you are looking at the trajectory of under constant acceleration; similarly $v_{0}$ is just the initial velocity of the trajectory. You can choose them to be whatever you want them to be. I can for example drop my object from a height of 5 meters from the ground, starting at rest, in which case $x_{0} = 5 \text{m}$ , $v_{0} = 0 \text{m /s}$ , and (ignoring air resistance) the equations of motion become $x(t) = 5 \text{m} - \frac{1}{2}gt^{2}$. Hope that helps friend!

3. May 2, 2013

### e-zero

Ok, is there an example where both x and x0 are both not zero?

4. May 2, 2013

### WannabeNewton

$x(t)$ is a function of time so it will change its value at every instant of time. In the example I gave above, $x(t)$ is the height of the particle from the ground so it will be non-zero up until the first time the particle hits the ground.

5. May 2, 2013

### e-zero

Can you give an example that does not involve vertical, but horizontal motion in which x and x0 are both not zero?

6. May 2, 2013

### WannabeNewton

Sure! Choose an origin and take a particle located 5 meters horizontally from that origin and give it an initial kick of 5 meters per second in the horizontal direction.

7. May 2, 2013

### e-zero

Ok. I was just confusing myself. It all depends on the question if you should take x0 to be zero or not.

8. May 2, 2013

### WannabeNewton

Indeed! Good luck with your studies friend :)

9. May 2, 2013

### e-zero

Thanks

10. May 2, 2013

### fluidistic

Not really. It depends on where you want the origin of your system of coordinates to be. In WBN's example, he chose the ground as origin. That's why x_0 in his case was 5m. For the same example he could have chosen its origin 5 meters above the ground, in which case x_0 would have been 0.

11. May 2, 2013

Ok, I see.