2.19 Exploring Acceleration

Acceleration Units:

Any combination of velocity and time units that follows the mathematical relationship shown in the acceleration equation can be used to express acceleration. For example: acceleration could be expressed in m/s/s, m/s^2, km/hr/s, cm/s/s, or cm/s^2. Also remember that since acceleration is a vector quantity, the direction of the acceleration would be included with the answer.

Sample Calculation of Acceleration:

Consider this problem: A ball starting from rest rolls forward to 40.0 cm/s in 4.00 seconds. Find the ball's acceleration. GIVEN a = ? vo = 0 cm/s vf = 40.0 cm/s t = 4.00 seconds WORK a = (vf - vo)/ change int a = (40.0 cm/s - 0 cm/s)/4.00 s a = 10.0 cm/s/s or 10.0 cm/s^2 ANSWER a = 10.0 cm/s/s or 10.0 cm/s^2 forward

Acceleration Equation:

The acceleration equation uses these symbols: "a" is the symbol for acceleration; "vo" is the original or initial velocity; "vf" is the final velocity; "t" is the time interval. The equation is as follows: a = (vf - vo)/change in t

Additional equations:

There are other equations that can be used for a uniformly accelerated object. You will remember that "d" is the symbol for change in position or displacement. d = vot + 1/2 at^2 vf^2 = vo^2 + 2ad a = (vf - vo)/t These equations are often used to calculate various quantities involving objects that are moved from a stopped or rest position or are dropped from a motionless or rest position. If the initial velocity of the object under consideration is zero, vo is eliminated from the equation. The equations become these: d = 1/2 at^2 vf^2 = 2ad a = vf/t or vf = at

Acceleration:

We can change the velocity of an object in three ways. We can *change the speed* of the object. We can *change the direction* in which the object is moving. Lastly, we can *change both the speed and direction* of the object. When we change the velocity of an object, the object undergoes *acceleration*. Acceleration is defined as the rate of change of velocity. Think about the accelerator in your car. When you press on the accelerator, the speed of the car increases. This increase in speed is an example of acceleration. Think about the brakes in your car. When you press on the brake, the speed of the car decreases. This decrease in speed is an example of acceleration. We often call this deceleration. Think about the steering wheel in your car. When you turn the steering wheel, you change the direction in which your car is moving. This change in direction is an example of acceleration. Most people think of "speeding up" when they use the term "acceleration." This is a very narrow perspective of acceleration. As you learned from this section, acceleration occurs when the velocity of something changes by changing its speed, its direction, or changing both speed and direction. Acceleration is a vector quantity.