1. Compare and contrast speed and yelocity. 2. What does acceleration measure? 3. Can you accelerate without changing your speed? 4. What is the slope of a line on a position-time graph? 5. What is the slope of a line on a velocity-time graph? 6. What is free fall? 7. Do objects of different masses hit the ground at the same time if they are dropped from the same height? 8. What is the quantity given to acceleration due to gravity? 9. Resolve the vector combinations below: a. \( \quad 45 \mathrm{~m} \mathrm{~S} \) and 35 m S b. \( \quad 15 \mathrm{mN} \) and 60 m s c. \( \quad 5 \mathrm{~m} \mathrm{~S} \) and 10 mE d. \( \quad 5 \mathrm{~m} \mathrm{~S}, 10 \mathrm{~m} \mathrm{E}, 7 \mathrm{~m} \mathrm{~W} \), and 10 m N 10. Calculate each of the following: a. What is the speed of a jet plane that travels 3000 m in 10 seconds? b. How long does it take for a long-distance runner to run the 10 km race if he travels at a velocity of \( 330 \mathrm{~m} / \mathrm{s} \) ? 11. Draw a graph of the following scenario and then calculate the acceleration for each segment: You are traveling down I-75 and you set the cruise control at 70 mph for 10 minutes, have to hit the brakes because someone cuts you off and slow down to 55 mph for 2 minutes, and then speed up to 75 mph for the remaining 5 minutes of your trip.

Let's address each of your questions step by step. ### 1. Compare and contrast speed and velocity. - **Speed** is a scalar quantity that refers to how fast an object is moving, regardless of its direction. It is defined as the distance traveled per unit of time. - **Velocity**, on the other hand, is a vector quantity that includes both the speed of an object and the direction of its motion. For example, a car traveling at 60 km/h to the north has a velocity, while a car traveling at 60 km/h without a specified direction only has speed. ### 2. What does acceleration measure? Acceleration measures the rate of change of velocity of an object over time. It indicates how quickly an object is speeding up, slowing down, or changing direction. ### 3. Can you accelerate without changing your speed? Yes, you can accelerate without changing your speed. This occurs when an object changes direction while maintaining a constant speed. For example, a car turning around a curve at a constant speed is accelerating because its direction is changing. ### 4. What is the slope of a line on a position-time graph? The slope of a line on a position-time graph represents the velocity of the object. A steeper slope indicates a higher velocity, while a flat line indicates that the object is at rest. ### 5. What is the slope of a line on a velocity-time graph? The slope of a line on a velocity-time graph represents acceleration. A positive slope indicates increasing velocity (acceleration), while a negative slope indicates decreasing velocity (deceleration). ### 6. What is free fall? Free fall is the motion of an object under the influence of gravity alone, with no other forces acting on it (like air resistance). In free fall, all objects accelerate downward at the same rate, regardless of their mass. ### 7. Do objects of different masses hit the ground at the same time if they are dropped from the same height? Yes, in a vacuum where there is no air resistance, objects of different masses will hit the ground at the same time when dropped from the same height. This is due to the uniform acceleration of gravity acting on all objects equally. ### 8. What is the quantity given to acceleration due to gravity? The acceleration due to gravity is commonly denoted as \( g \) and has a standard value of approximately \( 9.81 \, \text{m/s}^2 \) near the surface of the Earth. ### 9. Resolve the vector combinations below: To resolve the vector combinations, we will treat them as components in a coordinate system. a. \( 45 \, \text{m S} \) and \( 35 \, \text{m S} \): - Total South component: \( 45 + 35 = 80 \, \text{m S} \) b. \( 15 \, \text{m N} \) and \( 60 \, \text{m S} \): - Total North-South component: \( 15 \, \text{m N} - 60 \, \text{m S} = -45 \, \text{m S} \) (which means 45 m South) c. \( 5 \, \text{m S} \) and \( 10 \, \text{m E} \): - Resultant vector: \( \sqrt{(5^2 + 10^2)} = \sqrt{25 + 100} = \sqrt{125} = 11.18 \, \text{m} \) at an angle \( \tan^{-1}(5/10) = 26.57^\circ \) South of East. d. \( 5 \, \text{m S}, 10 \, \text{m E}, 7 \, \text{m W}, \) and \( 10 \, \text{m N} \): - North-South: \( 10 \, \text{m N} - 5 \, \text{m S} = 5 \, \text{m N} \) - East-West: \( 10 \, \text{m E} - 7 \, \text{m W} = 3 \, \text{m E} \) - Resultant vector: \( \sqrt{(5^2 + 3^2)} = \sqrt{25 + 9} = \sqrt{34} = 5.83 \, \text{m} \) at an angle \( \tan^{-1}(5/3) = 59.04^\circ \) North of East. ### 10. Calculate each of the following: a. Speed of a jet plane that travels 3000 m in 10 seconds: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{3000 \, \text{m}}{10 \, \text{s}} = 300 \, \text{m/s} \] b. Time for a long-distance runner to run 10 km at a velocity of \( 330 \, \text{m/s} \): \[ \text{Time} = \frac{\text{Distance}}{\text{Velocity}} = \frac{10000 \, \text{m}}{330 \, \text{m/s}} \approx 30.30 \, \text{s} \] ### 11. Draw a graph of the following scenario and then calculate the acceleration for each segment: To calculate the acceleration for each segment, we need to determine the change in velocity over time. 1. **First Segment**: 70 mph for 10 minutes (constant speed, so acceleration = 0). 2. **Second Segment**: Deceleration from 70 mph to 55 mph in 2 minutes. - Change in velocity: \( 70 - 55 = 15 \, \text{mph} \) - Time: 2 minutes = 120 seconds - Acceleration: \[ a = \frac{\Delta v}{\Delta t} = \frac{-15 \, \text{mph}}{120 \, \text{s}} = -0.125 \, \text{mph/s} \] 3. **Third Segment**: Acceleration from 55 mph to 75 mph in 5 minutes. - Change in velocity: \( 75 - 55 = 20 \, \text{mph} \) - Time: 5 minutes = 300 seconds - Acceleration: \[ a = \frac{\Delta v}{\Delta t} = \frac{20 \, \text{mph}}{300 \, \text{s}} \approx 0.067 \, \text{mph/s} \] ### Summary of Accelerations: - First Segment: \( 0 \, \text{mph/s} \) - Second Segment: \( -0.125 \, \text{mph/s} \) - Third Segment: \( 0.067 \, \text{mph/s} \) If