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# Physics Help in Motion Along A Straight-line

Everything in the world moves. *Everything*. Even objects that you think are seemingly stationary. Earth is rotating on it's axis, and orbits about the sun- all located in the milkyway galaxy, which is also in motion with other galaxies. This is a guide to help make studying for motion along a straight line, in your college physics course, a bit easier!

**Kinematics**: classifications and comparisons of motions.

Keep in mind: general properties of motion is restricted in three ways:

**motion is along a straight line only**(horizontal, vertical, diagonal)**forces cause motion**(pushes or pulls)**the moving object is either a particle**(point-like object, ex: electron)**or any object that moves like a particle**. (every portion of said object moves in the same direction and rate: tumbleweeds do NOT move like a particle)

## Displacement

**Displacement**- x, change in position. It is represented by the equation below, where the triangle is the uppercase delta symbol, indication change.

Displacement is a **vector **quantity, meaning it has BOTH **magnitude and direction!** The standard unit for displacement is a **meter**.

A positive result means the particle is moving in a positive directions, and vice versa for a negative result. If an object is going in the positive direction, it needn't be stated- BUT if the particle is going in the negative direction, you have to show it- in either words, or simply by a negative sign.

***Do NOT get this mix up with distance, which only shows the magnitude. Why?**

*Example)*

#### X_{1}= 10m and X_{2}= 100m

#### If a particle starts at position X_{1}, and then goes to X2,and then back to X_{1}, the particle is back at it's starting position and therefore:

**displacement = 0m**

**distance= 180m**

## Average Velocity

**Average Velocity:** ratio of displacement (delta x), that occurs in a time interval (delta t), as shown in the equation below.

Average velocity is a **vector **quantity. On a graph of x (position) versus t (time), the average velocity (v_{avg}) is the ** slope. **(Important)

The standard units for average velocity is **meters/second.**

## Average Speed

**Average Speed-** Instead of a particle's or object's displacement, we use the **total distance, **as displayed in the equation below.

Average speed has the same units as average velocity, meters/second, but average speed is NOT a vector quantity, because it doesn't include the direction. Be mindful of which equation to use, because using the wrong one will probably yield a wrong result.

## Instantaneous Velocity (or just velocity)

**velocity-** how fast a particle moves at a given instant, It is obtained from the average velocity. Acting as a limit, we shrink delta t closer and closer to 0 and as it gets smaller, the average velocity approaches a limiting value, aka the instantaneous velocity.

Velocity is a vector quantity- aka the sign is important. The standard units for velocity is m/s.

**Speed-** the magnitude of velocity. (no direction)

+7m/s and -7m/s, have the same speed of 7m/s, but different velocities, as indicated by the signs.

## Acceleration

**Acceleration**- when a particle's velocity changes, it undergoes acceleration. (If the velocity is constant, then the acceleration is 0.

The arrow above the a indicates that acceleration is a vector quantity. Its standard units are meters/second^{2} (m/s^{2}).

The **instantaneous ****acceleration**, is simply, the derivative velocity, and the second derivative of position.

** If the velocity and acceleration have different signs, the speed is decreasing. If they have the same signs, the speed is increasing.

## Constant Acceleration

*SPECIAL CASE EQUATIONS ** only use these equations if the acceleration is constant or approximately so.

## Free Fall Acceleration

the magnitude of free fall acceleration is 1 g, which is equivalent to approximately 9.8m/s^{2}.(This quantity varies based on latitude and seal level). If you're curious about what the gravitational acceleration is for your area, you can use **wolframaplha.com,** which calculates it for you. But most problems call for 9.80m/s^{2}.

Free fall acceleration in a problem is often presented with a ball or some object being through up in the air, and it comes back down.

It is important to understand that the acceleration an object is the same going up in the air and coming back down, 9.8m/s^{2}. Although, note, that the velocity changes. As you throw an object up, it has an initial velocity of v_{o. }Then it reaches it's maximum height and stops momentarily (v=o), and then returns back to earth with a final velocity, v.

## Sample Problems

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