Physics 1
Kinematics Notes
Acceleration


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What Acceleration Is:

Acceleration is the rate at which velocity changes. In other words, knowing the acceleration of an object tells you how fast the velocity of the object is changing.

[Definition of average acceleration]

Since velocity is the rate at which position changes, and acceleration is the rate at which velocity changes, acceleration is a "rate of a rate".

When Acceleration Happens:

It is very important to notice that acceleration is defined in terms of a change in velocity - not speed. This may seem like a minor point, but it isn't. Since acceleration is the rate velocity changes,

You are accelerating whenever you:

What Acceleration Isn't:

Since acceleration is linked to changes in velocity - when your velocity is changing, you are accelerating, students often get the misconception that "acceleration is a change in velocity". NO!! Acceleration is the rate at which the velocity changes - there's an important difference!

To say that "acceleration is a change in velocity" is like saying "velocity is a change in position" (This does sound silly, doesn't it?). Velocity tells you how fast position is changing. Acceleration tells you how fast velocity is changing.

Acceleration is not a change in velocity!

Calculating Accelerations:

Suppose a sprinter's velocity changes from 0 m/s to 10 m/s in 2 seconds at the start of a race. What is her acceleration?

[calculating acceleration]

Notice the odd units of acceleration - a distance (length) divided by 2 times. One time unit comes from the velocity in the numerator of the fraction, and the other comes from the denominator. Quantities like 4 mi/hr/sec are accelerations (4 mi/hr/sec means that the velocity changes by 4 mi/hr each second.).

Working With Accelerations:

Example:

A car starts from rest and accelerates at 2 m/s/s for 5 seconds. How fast will it be going?

Solution:

The statement "car starts from rest" means that the car's starting velocity is 0 m/s. An acceleration of 2 m/s/s means that the car's velocity changes by 2 m/s each second. If the car's velocity starts at 0 m/s and changes by 2 m/s in the first second, it will be going 2 m/s after 1 second has elapsed. During the second second (?!), its velocity increases by 2 m/s - from 2 m/s to 4 m/s. Its velocity will be 6 m/s after 3 seconds, 8 m/s after 4 seconds, and 10 m/s after 5 seconds.

Alternatively, there is a more-algebraic approach if you prefer. If [acceleration definition] then [velocity equation], so [problem solution]. If the velocity starts at 0 m/s and changes by 10 m/s, it ends at 10 m/s.

Specifying the Direction of an Acceleration:

Like velocity, accelerations in one-dimensional motions are positive if they act in the positive direction, and negative if they act in the negative direction. Determining the direction is a little more abstract for accelerations than velocities, however - at least until you get used to it.

There are 3 things to remember:


Example:

A car's velocity changes from +2 m/s to +10 m/s in 4 seconds. What is its acceleration?

Solution:

The car's change in velocity = ending velocity - starting velocity = 10 m/s - 2 m/s = 8 m/s. Its acceleration = its change in velocity divided by the time taken = (8 m/s)/(4 s) = 2 m/s/s.


Example:

A car's velocity changes from +10 m/s to +2 m/s in 4 seconds. What is its acceleration?

Solution:

The car's change in velocity = ending velocity - starting velocity = 2 m/s - 10 m/s = -8 m/s. Its acceleration = its change in velocity divided by the time taken = (-8 m/s)/(4 s) = -2 m/s/s.


Example:

A car's velocity changes from -2 m/s to -10 m/s in 4 seconds. What is its acceleration?

Solution:

The car's change in velocity = ending velocity - starting velocity = -10 m/s - (-2 m/s) = -10 m/s + 2 m/s = -8 m/s. Its acceleration = its change in velocity divided by the time taken = (-8 m/s)/(4 s) = -2 m/s/s.


Example:

A car's velocity changes from -10 m/s to -2 m/s in 4 seconds. What is its acceleration?

Solution:

The car's change in velocity = ending velocity - starting velocity = -2 m/s - (-10 m/s) = -2 m/s + 10 m/s = 8 m/s. Its acceleration = its change in velocity divided by the time taken = (8 m/s)/(4 s) = 2 m/s/s.


From these examples, notice that you just follow the (simple) rules - particularly remembering that the change in velocity is the ending velocity minus the starting velocity - NOT the big number minus the little number!

Calculating Accelerations When Only the Direction Changes:

In the examples above, you saw that it is pretty straightforward to calculate the acceleration of an object when its speed changes using algebra. An object also accelerates when its direction changes, but "normal" algebra is insufficient to calculate the acceleration in this case - you need to use vector algebra, and we will not bother with calculating these accelerations in this course.


Practice quiz on acceleration:

You need a Java-enabled browser to take a practic quiz on Newton's First Law.

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last update November 22, 2005 by JL Stanbrough