# Physics - Acceleration & Velocity - One Dimensional Motion

TLDRThe video script delves into the concepts of velocity and acceleration, clarifying their differences and how they relate to an object's motion. Velocity, described as the displacement over time, indicates how fast an object's position changes, while acceleration measures how quickly velocity changes. The script uses examples of a car and a truck to illustrate average and instantaneous velocity and acceleration, and provides formulas for calculating these quantities. It also covers unit conversions, such as from kilometers per hour to meters per second squared, and demonstrates how to apply these concepts in solving motion problems.

###### Takeaways

- π Velocity and acceleration are both vector quantities with magnitude and direction, but velocity describes the rate of change of position with respect to time, while acceleration describes the rate of change of velocity.
- π The formula for average velocity is the change in position (displacement) over time, and for instantaneous velocity, the time interval approaches zero.
- π£οΈ Speed is the rate of change of distance, whereas velocity is the rate of change of displacement, and they differ in that velocity includes direction.
- π The formula for average acceleration is the change in velocity over time, and for instantaneous acceleration, the time interval approaches zero.
- π To find the final velocity, use the equation v_final = v_initial + a * t, where 'a' is the acceleration and 't' is the time.
- π A car accelerating from 15 m/s to 45 m/s in 5 seconds has an average acceleration of 6 m/s^2.
- π A truck accelerating from 25 km/h to 45 km/h in 40 seconds has an average acceleration of 0.5 km/h/s or 0.13 m/s^2.
- π A car starting from rest with a constant acceleration of 3.5 m/s^2 will reach a speed of 42 m/s after 12 seconds.
- π A bus starting from 12 m/s and accelerating at 1.2 m/s^2 for 15 seconds will have a final speed of 30 m/s.
- ποΈ A sports car traveling at 95 mph and coming to rest in 4 seconds has an average acceleration of -10.6 m/s^2, indicating deceleration.

###### Q & A

### What is the main difference between velocity and acceleration?

-Velocity tells you how fast an object's position is changing with respect to time, while acceleration tells you how fast the velocity is changing.

### How is average velocity calculated?

-Average velocity is calculated using the formula v = (displacement) / (elapsed time), where displacement is the change in position (final position minus initial position).

### What does instantaneous velocity represent?

-Instantaneous velocity represents the velocity of an object at a specific moment in time, as opposed to the average velocity over a period of time.

### How can you find the final speed of an object undergoing constant acceleration?

-You can find the final speed using the equation v_final = v_initial + a * t, where v_initial is the initial speed, a is the acceleration, and t is the time.

### What is the formula for average acceleration?

-The formula for average acceleration is a = (v_final - v_initial) / t, where v_final is the final velocity, v_initial is the initial velocity, and t is the time interval.

### How do you calculate the acceleration of a car that accelerates from 15 m/s to 45 m/s in 5 seconds?

-The acceleration is calculated as a = (45 m/s - 15 m/s) / 5 s = 30 m/s / 5 s = 6 m/sΒ².

### A truck accelerates from 25 km/h to 45 km/h in 40 seconds. What is the average acceleration in km/h/s and m/sΒ²?

-The average acceleration is 0.5 km/h/s or 0.5 * (1000 m / 1 km) * (1 h / 3600 s) = 0.1389 m/sΒ².

### If a car accelerates from rest at a rate of 3.5 m/sΒ², what is its speed after 12 seconds?

-The speed of the car after 12 seconds is v_final = 0 + (3.5 m/sΒ² * 12 s) = 42 m/s.

### What is the final speed of a bus that accelerates from 12 m/s at a rate of 1.2 m/sΒ² for 15 seconds?

-The final speed of the bus is v_final = 12 m/s + (1.2 m/sΒ² * 15 s) = 30 m/s.

### A sports car traveling at 95 mph slams the brakes and comes to rest in 4 seconds. What is the average acceleration in m/sΒ²?

-The average acceleration is a = (0 - 42.47 m/s) / 4 s = -10.6175 m/sΒ², which is negative because the car is decelerating.

### How can you convert units from miles per hour to meters per second?

-To convert from miles per hour to meters per second, first convert miles to kilometers (1 mile β 1.60934 km), then convert hours to seconds (1 hour = 3600 seconds), and finally convert kilometers to meters (1 km = 1000 m). The formula is (mph * 1.60934) / 3.6.

###### Outlines

##### π Understanding Velocity and Acceleration

This paragraph introduces the concepts of velocity and acceleration, explaining that both are vector quantities with magnitude and direction. Velocity is defined as the rate of change of position with respect to time, calculated as the displacement over time. The difference between average velocity and instantaneous velocity is highlighted, with the latter being the velocity as time approaches zero. The paragraph uses the example of a car moving east at 30 miles per hour to illustrate the concepts of speed and velocity, emphasizing that speed is the rate of change of distance, while velocity is the rate of change of displacement. The relationship between these concepts is summarized by stating that speed indicates how fast the distance changes, while acceleration indicates how fast the velocity changes.

##### π Calculating Average Acceleration

The paragraph focuses on the calculation of average acceleration, which is the change in velocity over time. It provides a formula for calculating average acceleration and explains how to find the final speed given constant acceleration, initial speed, and time. The concept is illustrated with a problem where a car accelerates from 15 meters per second to 45 meters per second in five seconds, resulting in an average acceleration of 6 meters per second squared. The paragraph also discusses the importance of understanding the units of acceleration and how to convert between different units, such as from kilometers per hour per second to meters per second squared.

##### π Acceleration Problems and Solutions

This paragraph presents a series of problems involving acceleration, with detailed explanations and solutions. The first problem involves a truck accelerating from 25 kilometers per hour to 45 kilometers per hour in 40 seconds, resulting in an average acceleration of 0.5 kilometers per hour per second, which is then converted to 0.138 meters per second squared. The second problem concerns a car accelerating from rest at a rate of 3.5 meters per second squared, with the final speed calculated to be 42 meters per second after 12 seconds. The third problem involves a bus accelerating from 12 meters per second at a rate of 1.2 meters per second squared, reaching a final speed of 30 meters per second after 15 seconds. The final problem describes a sports car coming to rest in four seconds from 95 miles per hour, with an average acceleration of -10.6 meters per second squared, highlighting the negative sign indicating deceleration.

##### π Negative Acceleration and Deceleration

The final paragraph delves into the concept of negative acceleration, which is associated with deceleration. It explains how to calculate the average acceleration when a vehicle comes to a stop, using the example of a sports car traveling at 95 miles per hour that brakes to a halt in four seconds. The paragraph emphasizes the importance of converting units from miles per hour to meters per second for the calculation, resulting in an acceleration of -10.6 meters per second squared. This negative value signifies that the car is slowing down, and the paragraph reinforces the understanding that a negative acceleration corresponds to a decrease in speed.

###### Mindmap

###### Keywords

##### π‘Acceleration

##### π‘Velocity

##### π‘Displacement

##### π‘Speed

##### π‘Instantaneous Velocity

##### π‘Average Acceleration

##### π‘Final Speed

##### π‘Initial Speed

##### π‘Time Interval

##### π‘Constant Acceleration

##### π‘Unit Conversion

###### Highlights

The main difference between velocity and acceleration is that velocity describes how fast an object's position changes over time, while acceleration describes how fast the velocity changes.

Velocity is a vector quantity with both magnitude and direction, representing the displacement over time.

Acceleration is also a vector quantity, indicating the rate of change of velocity over time.

The formula for average velocity is the change in position (displacement) divided by the time taken.

Instantaneous velocity can be found by letting the time interval approach zero in the velocity equation.

Speed is the magnitude of velocity and does not include direction, whereas velocity does.

A car moving at 30 miles per hour east has a velocity of 30 mph to the east.

Acceleration is calculated as the change in velocity over time, which can be either average or instantaneous.

The formula for final velocity in constant acceleration scenarios is v_final = v_initial + a*t, where a is the acceleration and t is the time.

A car accelerating from 15 m/s to 45 m/s in 5 seconds has an average acceleration of 6 m/s^2.

A truck accelerating from 25 km/h to 45 km/h in 40 seconds has an average acceleration of 0.5 km/h/s or 0.13 m/s^2.

A car starting from rest and accelerating at 3.5 m/s^2 will reach a speed of 42 m/s after 12 seconds.

A bus accelerating from 12 m/s at 1.2 m/s^2 for 15 seconds will have a final speed of 30 m/s.

A sports car traveling at 95 mph and coming to rest in 4 seconds has an average acceleration of -10.6 m/s^2.

The negative acceleration indicates the car is slowing down, which is the case when the velocity decreases.

The concept of acceleration is central to understanding changes in velocity and is fundamental in physics and engineering.

Understanding the relationship between speed, velocity, and acceleration is crucial for analyzing motion and designing systems.

The examples provided in the transcript demonstrate the practical application of these concepts in real-world scenarios involving vehicles.

Unit conversion is an essential skill when dealing with different units of speed and acceleration, such as miles per hour and meters per second.

###### Transcripts

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