What does (change in velocity)/(change in time) mean?

Question

For example velocity = (change in position)/(change in time)

Answer 1

Change in * is shown as delta* in math talk. Delta means difference in two values. For example, delta x = x1 - x0, the difference (distance between) two x values; where x marks a position along the X axis in Cartesian coordinates. By similar reasoning, delta t = t1 - t0; the change in time...often called elapsed time.

We can write delta x/delta t = (x1 - x0)/(t1 - t0), which is the change in x position per change in time as the position changes. In other words delta t is the time elapsed when changing the x positions...how long it took to go from x0 to x1.

Similarly, we can also write delta v(x)/delta t; where v(x) is velocity in the x direction. Thus we have delta v(x)/delta t = (v1(x) - v0(x))/(t1 - t0). But look at this, we can write delta v(x)/delta t = a(x), which is, by definition, acceleration in the x direction. So your change in velocity/change in time is just acceleration because the velocity in the x direction is changing (speeding up or slowing down and/or changing direction) over some elapsed time.

This brings us to an important point. Most of the answers above were only half right. Most of them talked about changes in speed, but they failed to mention changes in direction.

Velocity and acceleration are vectors, which means they have both magnitude and direction. Velocity's magnitude is often called speed for example. But, to be a velocity, we also have to specifiy the direction of that speed. And, more to the point, when we specify a change in velocity, we need to specify the change in both its speed (its magnitude) and its direction.

Earlier we discussed v(x), velocity going in the easterly direction. But if that velocity were to turn to other than theta = 0 degrees (east) then there would be a change in direction even if the speed (its magnitude) does not change. There would be a change in velocity because of that change in direction. For example, going from 60 mph due east to 60 mph due north is a change in velocity.

In one of its basic forms, a velocity vector V = v(x) + v(y); where v(x) is the x direction velocity component of V and v(y) is the y direction component of V. The two vector components form the sides of a right triangle whose hypoteneuse has a magnitude |V| = sqrt(|v(x)|^2 + |v(y)|^2) and a direction theta = arctan(|v(y)|/|v(x)|). The symbol | | means magnitude; so |v(x)|, for instance, means magnitude of the x direction velocity.

Bottom line, when talking about change in velocity, you need to remember that means change in its magnitude and/or its direction.

Answer 2

Change in velocity is the end velocity (speed) minus the starting velocity.

for example:
If you were running 2mph and then increased to 5mph (miles per hour) then the CHANGE IN VELOCITY would be 3mph.

Same goes for time. If it was 3:15pm when you started running at 2mph, and then it was 3:30pm when you reached 5mph, then that was 15 minutes.

Answer 3

Speeding up or slowing down
For example, 0 to 60 mph in 0 to 6 seconds.

Answer 4

Yes,since acceleration is a vector it depends on both magnitude and direction.The best example in this case is the uniform circular motion where a body has only the radial acceleration and no tangential acceleration due to which the magnitude is constant but direction changes.

Answer 5

it means how much the speed change in a restricted time interval. In instance, people say it is an "acceleration" (or decceleration in the speed became slower than before).

Answer 6

acceleration

It you push the accelerator down for a couple of seconds and lets say your speed increases by a couple of miles per hour,
what are you doing?

Answer 7

its called ACCELERATION the change in velocity/ time a physcical unit of distance..

Answer 8

It's called 'acceleration'.

Doug

Answer 9

big juice