Physics III: Acceleration

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Physics III: Acceleration

Author: oLahav

This series of lessons is designed to help you learn, or review, the fundamentals of physics. It's time to get back to real motion, and look at acceleration.

Acceleration- the rate of change of the rate of change

The definition of acceleration is as follows:

Acceleration (a):

The rate of change of speed over time. Measured is metres per second squared.

This makes acceleration a second derivative- the rate of change of the rate of change of distance over time. Note that like velocity, acceleration is a vector and should have a direction associated with it.

Acceleration in formulas:

$a=\frac{v_{ave}}{t}$ . $v_{ave}$

is average velocity, so if we start at initial velocity

and end with final velocity of

then:

$a=\frac{v_f-v_i}{t}$ .

Other ways to represent the relationship between displacement, time, velocities and acceleration include:

, $d=v_it+\frac{at ^2}{2}$ ,

and manipulations of these.

Natural acceleration: gravity

Gravity (g):

The magnitude of the force of Earth's pull on objects.

$g=-9.8 \frac{m}{s ^2}$ .

Every object dropped accelerates at the exact same rate, regardless of its mass or size. Therefore, if two objects are dropped from the same height, they will reach the group at the same time (assuming air resistance is negligible). Try it at home!

Acceleration also occurs in non natural settings, such as when you step on the gas while driving your car. This is positive acceleration, since speed is increasing while you're moving forward. When you step on the break, you're moving forward but your speed is decreasing- that's negative acceleration, or deceleration.

How about those directions?

All changes in direction are classified as acceleration, since they represent a change in velocity.

On a 1D plane (going in one line), acceleration is uniform

when we change direction, since the acceleration moves us to that new direction.

However, if I turn right on a 2D plane, the acceleration may be non-uniform,

depending on whether we keep a constant radius or not. Circular motion

is a form of uniform acceleration. It's interesting to consider Jerk,

the third derivative of displacement and the rate of change of acceleration. However, this concept is not very useful and is mostly ignored in general physics studies.

Those were the basics of acceleration

Next time, we'll see an important application of acceleration that can be confusing- projectile motion.

Thanks for reading this Welcome to Physics Lesson!