Sunday, August 14, 2011

An Explanation of Acceleration

Can you accelerate without running faster?

Apparently you can.  This is why we started with distance v. displacement and moved on to speed v. velocity.  Acceleration is defined as the rate of change of velocity (not speed).

Linear Acceleration

Linear acceleration occurs as the athlete increases speed running down the vault runway (figure 7).

 Figure 7

Between positions #1 and #2, the athlete increases his velocity (speed toward the vault table) from 0 ft/s to 4 ft/s.  At each position, he has again increased his velocity, reaching 12 ft/s before he reaches the vaulting board.

acceleration = change in velocity / time

a = Dv / Dt

This explains accelerating by increasing speed.  You can however, accelerate without increasing your speed.

Constant Acceleration

 Figure 8
Go right back to the previous equation … Acceleration is a change in velocity and velocity has direction.  So, an athlete can run at a constant 5 ft/s and still accelerate.  Whenever an athlete changes direction, he is accelerating (figure 8).

Note the change in arrow direction for each position.  His change in displacement is not in a straight direction, but angular.  Thus his displacement, as a vector, is constantly changing.

Even though this athlete hasn’t changed his speed, he is constantly changing his direction, thus accelerating.  This is known as Constant Acceleration.

acceleration = change in velocity / time

a = Dv / Dt

These are the same equation.  They have a different result because v is a vector.

Changing Acceleration

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 Figure 9
But what happens if the athlete does increase his speed while running in circle?  This is called Angular Acceleration (figure 9).

This discussion is not yet ripe, so we’ll come back to angular acceleration later when we discuss rotation.

In the mean time, if your athlete starts demonstrating angular acceleration and cannot stop, I recommend using an elephant gun.