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2.4 Acceleration

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An airplane flying very low to the ground, just above a beach full of onlookers, as it comes in for a landing.
A plane decelerates, or slows down, as it comes in for landing in St. Maarten. Its acceleration is opposite in direction to its velocity. (credit: Steve Conry, Flickr)

Learning objectives

By the end of this section, you will be able to:

  • Define and distinguish between instantaneous acceleration and average acceleration.
  • Calculate acceleration given initial time, initial velocity, final time, and final velocity.

The information presented in this section supports the following AP® learning objectives and science practices:

  • 3.A.1.1 The student is able to express the motion of an object using narrative, mathematical, and graphical representations. (S.P. 1.5, 2.1, 2.2)
  • 3.A.1.3 The student is able to analyze experimental data describing the motion of an object and is able to express the results of the analysis using narrative, mathematical, and graphical representations. (S.P. 5.1)

In everyday conversation, to accelerate means to speed up. The accelerator in a car can in fact cause it to speed up. The greater the acceleration    , the greater the change in velocity over a given time. The formal definition of acceleration is consistent with these notions, but more inclusive.

Average acceleration

Average Acceleration is the rate at which velocity changes ,

a - = Δ v Δ t = v f − v 0 t f − t 0 , size 12{ { bar {a}}= { {Δv} over {Δt} } = { {v"" lSub { size 8{f} } - v rSub { size 8{0} } } over {t rSub { size 8{f} } - t rSub { size 8{0} } } } } {}

where a - size 12{ { bar {a}}} {} is average acceleration, v size 12{v} {} is velocity, and t size 12{t} {} is time. (The bar over the a size 12{a} {} means average acceleration.)

Because acceleration is velocity in m/s divided by time in s, the SI units for acceleration are m/s 2 size 12{"m/s" rSup { size 8{2} } } {} , meters per second squared or meters per second per second, which literally means by how many meters per second the velocity changes every second.

Recall that velocity is a vector—it has both magnitude and direction. This means that a change in velocity can be a change in magnitude (or speed), but it can also be a change in direction . For example, if a car turns a corner at constant speed, it is accelerating because its direction is changing. The quicker you turn, the greater the acceleration. So there is an acceleration when velocity changes either in magnitude (an increase or decrease in speed) or in direction, or both.

Acceleration as a vector

Acceleration is a vector in the same direction as the change in velocity, Δ v size 12{Dv} {} . Since velocity is a vector, it can change either in magnitude or in direction. Acceleration is therefore a change in either speed or direction, or both.

Keep in mind that although acceleration is in the direction of the change in velocity, it is not always in the direction of motion . When an object's acceleration is in the same direction of its motion, the object will speed up. However, when an object's acceleration is opposite to the direction of its motion, the object will slow down. Speeding up and slowing down should not be confused with a positive and negative acceleration. The next two examples should help to make this distinction clear.

A subway train arriving at a station. A velocity vector arrow points along the track away from the train. An acceleration vector arrow points along the track toward the train.
A subway train in Sao Paulo, Brazil, decelerates as it comes into a station. It is accelerating in a direction opposite to its direction of motion. (credit: Yusuke Kawasaki, Flickr)

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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