Acceleration: initial velocity, final velocity

Elapsed time

Acceleration is defined as the __rate__ at which the **velocity**__ changes__. Mathematically, a rate is a quantity divided by time. In this case, the quantity divided by time is the change in velocity. Mathematically, a change is defined by subtraction. So, given these facts, the equation used to determine acceleration is

When solving acceleration problems using the equation, "a" is acceleration, "vi" is initial or beginning velocity, "vf" is final velocity, and "t" is time. is the Greek letter "Delta". It means change. Here are three example problems.

Example 1: 4.0s after leaving a stoplight, Joe's car has a velocity of 20km/h. What is the acceleration of the car? Here is a diagram showing what happens in this problem.

Sitting at the stoplight the velocity of the car is 0km/h. When the stoplight turns green the car speeds up. after 4.0s the velocity of the car is now 20km/h. In this problem we have enough information to find the change in velocity ( 20km/h - 0km/h = 20km/h). Using the time it took for the velocity to change, we can now find the acceleration, 20km/h / 4.0s = 5km/h/s. The acceleration of the car during this first 4.0s after leaving the stoplight was 5km/h/s. Here is how __you__ would set this problem up.

What does this answer mean? It means that the velocity of the car increased by 5.0km/h during each second of motion after the light turned green. This only describes what happened to the car during the first 4.0seconds after the light turned green. We have no idea what happened after 4.0seconds. __Also note that the velocity part of the answer does NOT have to have the same time unit as the time of motion. Here the change in velocity is in km/h while the time of motion is in seconds.__ This is a positive acceleration. Positive acceleration means speeding up.

Example 2: An F-18 Hornet with a velocity of 230km/h, landing on the deck of an aircraft carrier, comes to a complete stop in 2.0s. What is the acceleration of the jet?

In this problem the initial velocity, 230km/h is greater than the final velocity, 0km/h. This means that when the change in velocity is calculated, the result will be a negative number ( 0km/h - 230km/h = -230km/h), The final answer is determined by dividing this change in velocity by the time (-230km/h / 2.0s ). The answer is -115 km/h/s. Hear is how you should set this problem up.

Like the car problem in example #1, the time unit is not the same as in the velocity part of the problem. The negative sign in the answer means that the jet is slowing down or decelerating. __Negative acceleration means slowing down.__

Example 3: A rocket traveling at 300m/s slows to 100m/s in 7.0s when the rocket motor stops. What is the acceleration of the rocket.

Here is how we can set this problem up:

There are several things to make note of in this example. First, unlike the last two examples, the unit of time in the velocity part of this problem __is the same__ as the time unit in the denominator. The unit of acceleration can be expressed in two ways, meters per second per second (m/s/s), or meters per second squared m/s2). In the SI system scientists work in **Kg m s **units, using **k**ilograms for mass, **m**eters for length, and** s**econds for time. This derived unit, __m/s/s or m/s__2__ is the standard unit for measuring acceleration in the SI system of measurement__. Also, note that the rocket was traveling at an initial velocity that was greater than the final velocity. The rocket slowed down so it experienced a negative acceleration.