All work should be done on your own sheet of paper. Some of the answers are provided so that you can check your work. Kinematics & Free Fall Problems - lyeranti moore 1. Define each of the following physical quantities in your own words. Indicate what units are used to measure each quantity in the SI system. Displacement: Velocity: Acceleration: 2. A car travels 17 km due east then does a U-turn and travels 23 km due west. a) What total distance has the car traveled? b) What is the total displacement of the car? c) If the entire trip took 2.0 hours, determine the average speed of the car. Give your answer in both km/hour, and m/s (show conversion) d) If the entire trip took 2.0 hours, determine the average velocity of the car. Give your answer in both km/h and mph. (show conversion) 3. Write down each of the following formulas: a) Constant speed motion b) No'v' formula c) No'd' formula d) No't' formula e) No'a' formula For each of the following problems be sure to:List known & unknown quantities, write the formula, box answer with 2-3 significant digits and correct units. 4. A car decelerates uniformly from 24m/s to 18m/s in 3.0 seconds. How far does it travel during this time? d=63m 5. A car is initially traveling at 17m/s when the driver steps down hard on the gas pedal resulting in an acceleration of 3.0m/s^2 How fast will the car be moving 4.0 seconds later? v=29m/s 6. A car initially traveling at 24m/s slams on the brakes and moves forward 196 m before coming to a complete halt. What was the magnitude of the car's deceleration? a=1.47m/s^2 7. A bike that is coasting down a steep hill increases its speed from 8.0m/s to 14m/s The length of the hill is 55 meters. How much time passes during the descent? t=5s 8. How long does it take a hiker to walk 7.0 miles if her average speed is 2.0 miles per hour? t=3.5hr 9. Ifa car's brakes can decelerate the car at a rate of 8.0m/s^2 what is the minimum stopping distance of a car that is initially traveling 20.0m/s d=25 m

# Brief Explanations:<br />Displacement is the straight-line distance between the initial and final positions, measured in meters (m). Velocity is the rate of change of displacement, measured in meters per second (m/s). Acceleration is the rate of change of velocity, measured in meters per second squared (m/s²).<br /><br /># Answer:<br />1. Define each of the following physical quantities in your own words. Indicate what units are used to measure each quantity in the SI system.<br /> - Displacement: The straight-line distance between the initial and final positions of an object, measured in meters (m).<br /> - Velocity: The rate at which an object changes its position, measured in meters per second (m/s).<br /> - Acceleration: The rate at which an object's velocity changes over time, measured in meters per second squared (m/s²).<br /><br />2. A car travels 17 km due east, then does a U-turn, and travels 23 km due west.<br /> a) What total distance has the car traveled?<br /> - The total distance is the sum of the distances traveled in each direction.<br /><br /> # Brief Explanations:<br /> The total distance is the sum of all distances traveled, regardless of direction.<br /><br /> # Answer:<br /> a) 40 km<br /><br /> b) What is the total displacement of the car?<br /> - Displacement is the straight-line distance from the starting point to the final position.<br /><br /> # Brief Explanations:<br /> Displacement considers direction and is the difference between the final and initial positions.<br /><br /> # Answer:<br /> b) 6 km west<br /><br /> c) If the entire trip took 2.0 hours, determine the average speed of the car. Give your answer in both \( \mathrm{km} / \) hour, and \( \mathrm{m} / \mathrm{s} \). (show conversion)<br /> - Average speed is total distance divided by total time.<br /><br /> # Brief Explanations:<br /> Average speed = Total distance / Total time. Convert km/h to m/s by multiplying by (1000 m / 1 km) and dividing by (3600 s / 1 hr).<br /><br /> # Answer:<br /> c) 20 km/h, 5.56 m/s<br /><br /> d) If the entire trip took 2.0 hours, determine the average velocity of the car. Give your answer in both \( \mathrm{km} / \mathrm{h} \), and mph. (show conversion)<br /> - Average velocity is total displacement divided by total time.<br /><br /> # Brief Explanations:<br /> Average velocity = Total displacement / Total time. Convert km/h to mph by multiplying by (0.621371 mi / 1 km).<br /><br /> # Answer:<br /> d) 3 km/h west, 1.86 mph west<br /><br />3. Write down each of the following formulas:<br /> a) Constant speed motion: \( v = \frac{d}{t} \)<br /> b) No ' \( v \) ' formula: \( d = v_i t + \frac{1}{2} a t^2 \)<br /> c) No 'd' formula: \( v_f = v_i + a t \)<br /> d) No 't' formula: \( v_f^2 = v_i^2 + 2 a d \)<br /> e) No 'a' formula: \( d = \frac{(v_i + v_f)}{2} t \)<br /><br />4. A car decelerates uniformly from \( 24 \mathrm{~m} / \mathrm{s} \) to \( 18 \mathrm{~m} / \mathrm{s} \) in 3.0 seconds. How far does it travel during this time? \( d=63 \mathrm{~m} \)<br /> - Use the formula \( d = \frac{(v_i + v_f)}{2} t \).<br /><br /> # Brief Explanations:<br /> Average velocity = (Initial velocity + Final velocity) / 2. Distance = Average velocity * Time.<br /><br /> # Answer:<br /> 63 m<br /><br />5. A car is initially traveling at \( 17 \mathrm{~m} / \mathrm{s} \) when the driver steps down hard on the gas pedal resulting in an acceleration of \( 3.0 \mathrm{~m} / \mathrm{s}^{2} \). How fast will the car be moving 4.0 seconds later? \( \mathrm{v}=29 \mathrm{~m} / \mathrm{s} \)<br /> - Use the formula \( v_f = v_i + a t \).<br /><br /> # Brief Explanations:<br /> Final velocity = Initial velocity + (Acceleration * Time).<br /><br /> # Answer:<br /> 29 m/s<br /><br />6. A car initially traveling at \( 24 \mathrm{~m} / \mathrm{s} \) slams on the brakes and moves forward 196 m before coming to a complete halt. What was the magnitude of the car's deceleration? \( \mathrm{a}=1.47 \mathrm{~m} / \mathrm{s}^{2} \)<br /> - Use the formula \( v_f^2 = v_i^2 + 2 a d \).<br /><br /> # Brief Explanations:<br /> Rearrange to solve for acceleration: \( a = \frac{v_f^2 - v_i^2}{2d} \).<br /><br /> # Answer:<br /> 1.47 m/s²<br /><br />7. A bike that is coasting down a steep hill increases its speed from \( 8.0 \mathrm{~m} / \mathrm{s} \) to \( 14 \mathrm{~m} / \mathrm{s} \). The length of the hill is 55 meters. How much time passes during the descent? \( \mathrm{t}=5 \mathrm{~s} \)<br /> - Use the formula \( d = \frac{(v_i + v_f)}{2} t \).<br /><br /> # Brief Explanations:<br /> Rearrange to solve for time: \( t = \frac{2d}{v_i + v_f} \).<br /><br /> # Answer:<br /> 5 s<br /><br />8. How long does it take a hiker to walk 7.0 miles if her average speed is 2.0 miles per hour? \( t=3.5 \mathrm{hr} \)<br /> - Use the formula \( t = \frac{d}{v} \).<br /><br /> # Brief Explanations:<br /> Time = Distance / Speed.<br /><br /> # Answer:<br /> 3.5 hr<br /><br />9. If a car's brakes can decelerate the car at a rate of \( 8.0 \mathrm{~m} / \mathrm{s}^{2} \), what is the minimum stopping distance of a car that is initially traveling \( 20.0 \mathrm{~m} / \mathrm{s} ? \mathrm{~d}=25 \mathrm{~m} \)<br /> - Use the formula \( v_f^2 = v_i^2 + 2 a d \).<br /><br /> # Brief Explanations:<br /> Rearrange to solve for distance: \( d = \frac{v_f^2 - v_i^2}{2a} \).<br /><br /> # Answer:<br /> 25 m