can u show me the fraction formula- . Key Concepts of Motion (Including Velocity)

Question

Speed vs. Velocity:
Speed: Speed tells you how fast an object is moving, but it does not tell you the direction. It’s a scalar quantity, meaning it only has magnitude (size) and no direction. For example, if a car is moving at 60 km/h, we only know how fast it's moving, not in which direction.
Formula: Speed=DistanceTime\text{Speed} =
Velocity: Velocity is similar to speed, but it includes both magnitude (how fast) and direction. This makes it a vector quantity. For example, a car moving at 60 km/h north has a specific velocity because it’s not just a speed (60 km/h) but also a direction (north).
Formula for velocity:
Velocity=DisplacementTime\text{Velocity} = \frac{\text{Displacement}}{\text{Time}}Velocity=TimeDisplacement​
Where displacement is the straight-line distance between the starting and ending points, with direction.
Example: If a car moves 100 meters north in 5 seconds, its velocity is:
Velocity=100 m North5 s=20 m/s North\text{Velocity} = \frac{100 \, \text{m North}}{5 \, \text{s}} = 20 \, \text{m/s North}Velocity=5s100m North​=20m/s North
The important difference between speed and velocity is that velocity has direction. This means two objects can have the same speed but different velocities if they are moving in different directions.

2. Rest, Constant Speed, and Acceleration
Rest (No Motion):
Rest is when an object is not moving, meaning its speed and velocity are both zero.
On a distance-time graph, rest is shown as a flat horizontal line, as no distance is covered.

Constant Speed (No Acceleration):
When an object is moving at a constant speed, its velocity doesn’t change.
On a distance-time graph, constant speed is represented by a straight line with a constant slope (the slope shows the speed).
Constant velocity means there’s no acceleration, and the object is traveling in a straight line in a constant direction.

Acceleration:
Acceleration is the change in velocity (either a change in speed or direction) over time. The object could either speed up, slow down, or change direction.
Formula for acceleration:
Acceleration=Change in velocityTime\text{Acceleration} = \frac{\text{Change in velocity}}{\text{Time}}Acceleration=TimeChange in velocity​
Positive acceleration: When an object speeds up.
Negative acceleration (deceleration): When an object slows down.
Example: If an object changes its velocity from 0 m/s to 20 m/s in 5 seconds, its acceleration is:
Acceleration=20 m/s−0 m/s5 seconds=4 m/s2\text{Acceleration} = \frac{20 \, \text{m/s} - 0 \, \text{m/s}}{5 \, \text{seconds}} = 4 \, \text{m/s}^2Acceleration=5seconds20m/s−0m/s​=4m/s2

Answer 1

Certainly! Here are the fraction formulas for speed, velocity, and acceleration, presented clearly:

1. Speed Formula

Speed is defined as the distance traveled divided by the time taken. The formula is:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

2. Velocity Formula

Velocity, like speed, is the distance traveled per unit time, but it also incorporates direction. The formula is:

\[ \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} \]

Where:

• Displacement is the straight-line distance between the starting and ending points, considering direction.

3. Acceleration Formula

Acceleration is the change in velocity per unit time. The formula is:

\[ \text{Acceleration} = \frac{\text{Change in velocity}}{\text{Time}} = \frac{\Delta v}{\Delta t} \]

Where:

• \(\Delta v\) is the change in velocity, which can be calculated as the final velocity minus the initial velocity (\(v_f - v_i\)).
• \(\Delta t\) is the change in time.

Examples

Here’s an example for each formula based on the descriptions you provided:

1. Speed Example: If a car travels 120 km in 2 hours, then its speed is:

   \[ \text{Speed} = \frac{120 \text{ km}}{2 \text{ hours}} = 60 \text{ km/h} \]

2. Velocity Example: If a car moves 100 meters north in 5 seconds, its velocity is:

   \[ \text{Velocity} = \frac{100 \text{ m North}}{5 \text{ s}} = 20 \text{ m/s North} \]

3. Acceleration Example: If an object changes its velocity from 0 m/s to 20 m/s in 5 seconds, its acceleration is:

   \[ \text{Acceleration} = \frac{20 \text{ m/s} - 0 \text{ m/s}}{5 \text{ seconds}} = 4 \text{ m/s}^2 \]

These formulas are fundamental in analyzing motion in physics! If you have more questions or need further explanations, feel free to ask.