How to calculate gradually increasing speed when time and distance is known? How do I calculate this? How much does the speed need to increase in second in order to reach the destination in 10 seconds? Speed starts at 0.
Distance to reach = 1000 meters
Time to reach distance = 10 seconds
Speed increment in second = ?

I've been banging my head against the wall for the past few hours, since I just can't figure this out and can't find any help from google... I don't even know if this is a valid question anymore, I am losing hope. I am clearly not that good in math. Sorry if I have the wrong tag on the question, I have no idea what category this question is related to.
 A: You are looking for speed increment, which I find a badly worded expression for what is known as acceleration.
Acceleration is the rate of change of speed. In your example we are assuming that acceleration is constant, and so speed increases from zero up by a constant amount every second. Note that here we are measuring speed in meters per second ($\frac ms$). So our unit for measuring acceleration is meters per squared second ($\frac{m}{s^2}$).
Now, you can solve your problem using mechanics of motion in one dimension. There are a bunch of formulas that describe this kind of motion. We choose the one that works with the data we have. Here we have the distance and time, and we want to find acceleration. Here is the formula:
$$x = \frac12 a \; t^2$$
where $x$ is distance ($m$), $a$ is acceleration ($\frac{m}{s^2}$) and $t$ is time ($s$). You can take it from here, right?
A: I was able to calculate acceleration using that formula which Saeed and John Douma posted. I would have never been able to calculate this without help from my relative, since my math understanding is pretty much limited to elementary school math. But here is the whole answer:
$$x = \frac12 a \; t^2$$
$$\frac{x}{\frac12} = at^2$$
$$\frac{\frac{2x}{t^2}}{t^2} = a$$
$$a = \frac{2x}{t^2}$$
$$acceleration = \frac{2\cdot distance}{time^2}$$
