Search results
16 wrz 2015 · Sep 17, 2015. v = dx dt. This means that the velocity over a certain period of time is the instantaneous change in position (dx) over the instantaneous change in time (dt). This period of time is intentionally very small, hence "instantaneous".
An easy way to remember the formulae is to put distance, speed and time (or the letters D, S and T) into a triangle. The triangles will help you remember these three rules: \(Distance = Speed ...
The integral of acceleration over time is change in velocity (∆v = ∫a dt). The integral of velocity over time is change in position ( ∆ s = ∫ v dt ). Here's the way it works.
What is the speed distance time triangle? The speed distance time triangle is a way to describe the relationship between speed, distance and time as shown by the formula below. \textbf {Speed } \bf {=} \textbf { distance } \bf {\div} \textbf { time} “Speed equals distance divided by time”.
Each equation contains four variables. The variables include acceleration (a), time (t), displacement (d), final velocity (vf), and initial velocity (vi). If values of three variables are known, then the others can be calculated using the equations.
The left-hand side \(d v / d t\) is just the acceleration \(a_{c}\); the second factor on the right-hand side \(d r / d t\) is the velocity \(v\). Therefore this equation becomes \[a_{c}=\frac{v^{2}}{r}\]
If there is no acceleration, we have the formula: s = v t where s is the displacement, v the (constant) velocity and t the time over which the motion occurred. This is just a special case ( a = 0 ) of the more general equations for constant acceleration below.
