The acceleration of an object is its change in velocity divided by the time the change takes.

acceleration = change in velocity\time interval:

The graph below might be the change in velocity of a skier who is moving downhill at a constant acceleration:

The skier starts at time = 0 with a velocity = 0. After 1 second, the velocity is 0.5 m/s. After 2 seconds, the velocity has increased to 1 m/s. For every second, the velocity increases by 0.5 m/s. We can say that the change in velocity is constant and equal to 0.5 m/s every second. This can be written as 0.5 m/s/s, or 0.5 m/s2.

The **area** under the velocity-time graph is the displacement. The above graph of constant acceleration forms a triangle between the velocity curve and the time axis. The area of a triangle is half its height times its base: 0.5 x 6 m/s x 12 s = 36m.

The slope of the velocity-time graph is the acceleration. The steeper the slope, the greater the acceleration. To find the slope, choose any two points: slope =

Consider the motion of a car between traffic lights:

What would this motion look like in a graph of velocity against time?

Question: What is the acceleration in the first two seconds?

Answer: initial velocity .

Final velocity .

Therefore,

Using the formula

Note that 30 km/h can be expressed as m/s, by dividing by 3.6

Question: What is the acceleration in the last two seconds?

Answer: initial velocity .

Final velocity .

Therefore,

Using the formula

The acceleration is equal in magnitude to phase A, but opposite in direction (deceleration).

Question: What is the total displacement travelled by the car in the ten seconds?

Answer: the displacement is the area under the velocity curve. This is in three parts, A, B, and C.

First we need to convert 60 km/h into m/s so that the unit of time matches.

60 km/h /3.6 = 16.7 m/s

Area A: 0.5 ⋅ v ⋅ t = 0.5 ⋅ 16.7 m/s ⋅ 2 s = 16.7 m

Area C is the same as A

Area B: in this case, there is zero acceleration, but constant velocity. In this case, we use the formula

Total displacement = total area =

Content © Andrew Bone. All rights reserved. Created : July 13, 2013 Last updated :February 27, 2016

The most recent article is:

Air Resistance and Terminal Velocity

View this item in the topic:

and many more articles in the subject:

Science resources on ScienceLibrary.info. Games, puzzles, enigmas, internet resources, science fiction and fact, the weird and the wonderful things about the natural world. Have fun while learning Science with ScienceLibrary.info.

1896 - 1937

Wallace Carothers was an American chemist and pioneer in pure research into large-molecular weight polymers.

Website © contentwizard.ch | Designed by Andrew Bone