High School Physics/Velocity

Velocity is a concept that combines the ideas of speed and direction. A velocity, thus, is comprised of two components. The magnitude of the velocity is the instantaneous speed at a particular point in time. The direction component can be expressed in a number of ways. Traditionally, we may express the direction in terms of the points of a compass (North, South-West). However, it is common in Physics and Mathematics to use an angle (either in degrees or radians).

The average velocity is similar to the idea of an average speed, but deals instead with the total displacement (as opposed to distance travelled) and is expressed as:

$$v_a=\frac{\Delta x}{\Delta t}$$

For example, a runner who completes a lap of a 400m running track in 1 minute will have a total displacement of 0m, even though they have run 400m. Their average velocity, therefore is zero,

It correlates with acceleration,so if someone is constantly accelerating at a speed of 10cm/s and have been running for 10 seconds, their speed will be...

In which $$\rm Time\cdot Acceleration=Speed$$


 * $$t$$ = time running
 * $$a$$ = acceleration rate
 * $$s$$ = speed.

So with the previous example,

$$\rm 10s\cdot 10\frac{cm}{s^2}=100\frac{cm}{s}$$

If you are accelerating with a speed that is growing by 10cm/s,the formula would be

$$((at)+a)\cdot\frac{t}{2}=x$$

so if one were gaining 10cm/s in their speed per second while keeping their current speed...

$$((10\cdot 10)+10)\cdot\frac{10}{2}=500\rm cm$$

For variety of values,lets say the acceleration only lasted 5 seconds...

$$((5\cdot 10)+10)\cdot\frac{5}{2}=500\rm cm$$