# 63 Accelerated Motion

# Acceleration

After the becomes large enough to balance out a skydiver’s , they will have no . From we already know that an object’s prevents a change in unless it experience a net force, so from that point when the forces are balanced and onward, the skydiver continues at a until they open their parachute.

During the initial part of a skydive, before the is large enough to balance out the weight, there is a so their changes. The rate at which the velocity changes is known as the . Note that students often confuse velocity and acceleration because they are both rates of change, so to be specific: *velocity defines the rate at which the position is changing and acceleration defines the rate at which the velocity is changing. * We can calculate the (** a**) during a certain time interval (

*Δt*) by subtracting the (

**) from the (**

*v*_{i}**) to get the change in velocity (**

*v*_{f}**) and then dividing by the time interval (**

*Δv**Δ*t):

(1)

### Everyday Example

Let’s calculate the during the roughly 2 seconds it takes a parachute to fully open and slow a skydiver from 120 **MPH** to 6.0 **MPH**. First let’s remember that the skydiver is moving in our negative direction so the initial and final velocities should be negative. Also, lets convert to meters per second: and .

Starting with our definition of acceleration:

Inserting our values:

The two negatives in front of the 54 **m/s** make a positive, and then we calculate a value.

We now get a chance to see that the units of are **m/s/s** or equivalently **m/s ^{2}**

# Acceleration Direction

The direction of depends on the direction of the change in . If the velocity becomes more negative, then acceleration must be negative. This is the case for our skydiver during the first part of the jump; their speed is increasing in the negative direction, so their velocity is becoming more negative and therefore acceleration is negative. Conversely, if an object moves in the negative direction, but slows down, the acceleration is positive, *even though the velocity is still negative*! This was the case for our skydiver just after opening their parachute, when they still moved downward, but were slowing down. Slowing down in the negative direction means the velocity is becoming less negative, so the acceleration must be positive. All of the possible combinations of direction and change and the resulting are summarized in the following chart:

Initial direction of motion ( initial velocity direction) | Speed change | Direction of Acceleration |

positive | speeding up | positive |

positive | slowing down | negative |

negative | speeding up | negative |

negative | slowing down | positive |

### Reinforcement Exercises

a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid

the force of gravity on on object, typically in reference to the force of gravity caused by Earth or another celestial body

the total amount of remaining unbalanced force on an object

an object's motion will not change unless it experiences a net force

the tenancy of an object to resist changes in motion

a quantity of speed with a defined direction, the change in speed per unit time, the slope of the position vs. time graph

not changing, having the same value within a specified interval of time, space, or other physical variable

a force applied by a fluid to any object moving with respect to the fluid, which acts opposite to the relative motion of the object relative to the fluid

the change in velocity per unit time, the slope of a velocity vs. time graph

average change in velocity per unit time, calculated as change in velocity during a time interval divided by the time interval

the value of velocity at the start of the time interval over which motion is being analyzed

the value of velocity at the end of the time interval over which motion is being analyzed

distance traveled per unit time