Acceleration can be determined from a velocity vs.time graph by calculating the line's______?

Question

Acceleration can be determined from a velocity vs.time graph by calculating the line's______?

Answer 1

Slope

Answer 2

The line's gradient, or slope.

Acceleration is defined as the change in velocity per unit time.  Normally we talk about a car's speed as opposed to velocity, which isn't strictly correct, but to show the velocity we'd have to show the direction th car was headed in as well, maybe not a problem if you have a SatNav, but probably complicating matters a litle too much.

For example, car manufacturers enjoy quoting the figures for cars to go from 0m.p.h to 60m.p.h (especially sports car manufacturers), they mean the time it takes for the initial velocity of 0m.p.h, to change to 60m.p.h, this is a measure of the cars' acceleration capabilities.

If you draw a line plotting the velocity of the car from when it starts from velocity A (in this example, at rest) to when it reaches velocity B (in this example 60m.p.h) against the time it's taken to do so, you'll get a line which may be a nice constant slope, as you'd hope, or perhaps it'd be jittery, if the driver (or the engine, or even the road conditions) is a little inconsistent.  Taking the gradient of this line between any two points will tell you how fast the car was accelerating during that time period.

Gradient (M) of a straight line (remember that, even if the line isn't straight all the way through, we can break it down into little areas which ARE straight, and use those as the calcuation points) is defined as the vertical (y-axis) change (which would give us the velocity change) over the horizontal (x-axis) change (which would give us the time change, or duration as it's known).

Like this : M = (Y final - Y initial) / (X final - X initial)

Which is just : Change in V / Change in T

Which is acceleration.