DISTANCE AND DISPLACEMENT 1. Determine the distance and displacement of the following: 1 st 1 st 2 nd 1 st 2 nd 1 st 2 nd 1 st 2 nd
2. Determine the speed and velocity of the following: 1 st (10 seconds) 1 st (30 seconds) 2 nd (50 seconds) 1 st (80 seconds) 2 nd (45 seconds) 1 st (25 seconds) 2 nd (10 seconds) 2 nd (7 sec) 1 st (5 sec) 3. When are distance and displacement different? 4. When are speed and velocity different? AVERAGE SPEED AND VELOCITY
5. You walk from your home to the library, then to the park. a. What is the distance traveled? [1.95 mi] If it takes 190 seconds what is your speed? [0.01 m/s] b. What is your displacement? [0.75 mi] If it takes 190 seconds what is your velocity? [0.004 m/s] 6. Ignoring the curves.you start at A and run to B in 45 seconds. a. What is your speed? [2.88 m/s] b. What is your velocity? [2.22 m/s]
7. You start at home.you walk to the park in 150 seconds. You hangout at the park for 80 seconds. You then run to your friend s house in 90 seconds. What is you average velocity for the whole trip? 75 m 80 m 30 m [0.578 m/s] 8. You travel 250 m in 88 seconds. Then travel 550 m (opposite direction) in 287 seconds. a. What is the total distance traveled? [800 m] b. What is your average velocity? [-0.80 m/s]
9. A car goes 1500 m in 55 seconds. How long does it take to travel 7000 m if it s average velocity for the entire trip is 40 m/s? [158 s] ACCELERATION PROBLEMS 10. If an object accelerates from rest, with a constant acceleration of 3.4 m/s 2, what will its velocity be after 28 s? [95.2 m/s]
11. A train departs from its station at a constant acceleration of 5 m/s 2, what is the speed of the train after going 60 m? [24.5 m/s] 12. An object starts at rest and accelerates at 9.8 m/s 2 for 3 seconds. How far will it travel? [44.1 m]
13. An object is traveling at a constant velocity of 15 m/s when it experiences an acceleration of -3.5 m/s 2. How long will it take to stop? [4.29 s] 14. A bicyclist is traveling at a speed of 5 m/s when it suddenly accelerates, at a constant rate of 0.6 m/s 2, for a time of 10 s. What is the speed of the bicycle at the end of that 10s? [11 m/s]
15. An object is traveling at a velocity of 15 m/s when it experiences a constant acceleration of 3.5 m/s 2 for a distance of 10 m. What will its velocity be after that acceleration? 16. A car's speedometer reads 20 m/s after accelerating, from a standing start, for 25s. What was its acceleration? [17.2 m/s] [+0.8 m/s]
17. An object s velocity goes from 36 m/s to 22 m/s in 5 s. What is the acceleration of the object? [-2.8 m/s 2 ] 18. An object initially at rest experiences an acceleration of 9.8 m/s 2. How much time will it take it to achieve a velocity of 58 m/s? [5.92 s]
19. An object is moving at a velocity of 23 m/s. It accelerates to a velocity of 85 m/s over a time of 8.3 s. What acceleration did it experience? How many g s is this? [7.46 m/s 2 = 0.76 g s] 20. A car is driving at a velocity of 24 m/s. If its brakes can supply an acceleration of -5.0 m/s 2, how much time will be required to bring the car to a stop? [4.8 s]
21. A car is driving at a velocity of 35 m/s. If its brakes can supply an acceleration of -3.0 m/s 2, how much distance will be required to bring the car to a stop? 22. A car accelerates at 5.0 m/s 2 from a velocity of 20 m/s to velocity of 28 m/s. Determine the distance it traveled. [204 m] [38.4 m]
23. A sports car accelerates from rest to 27.8 m/s in 6.2 s. Calculate its acceleration in m/s 2. How many g's in this (1 g = 9.8m/s 2 )? [+4.48 m/s 2 ] [0.46 g s] 24. A car decelerates from a speed of 30.0 m/s to rest in 8.0 s. Calculate the distance that the traveled during this time. [120. m]
25. In coming to a stop, a car leaves skid marks on the highway 450 m long. Assuming a deceleration of 10 m/s 2, estimate the speed of the car just before braking. [95 m/s] MULTISTEP PROBLEMS 26. A car starts from rest and accelerates at 0.85 m/s 2 for 19 seconds. It then travels at a constant speed for 30 seconds. a. What was the final velocity of the car after accelerating?[16.2 m/s] b. How much distance (total) will it travel? [639 m]
27. A car starts from rest and accelerates at 2.2 m/s 2 for 12 seconds. It then travels at a constant speed for 80 seconds. a. What was the final velocity of the car after accelerating? [26.4 m/s] b. How much distance (total) will it travel? [2270 m] c. After traveling that distance the car is stopped in 0.5 seconds. What was it acceleration during stopping? [-52.8 m/s 2 ] 28. A car starts from rest and accelerates at 2 m/s 2 for 10 seconds. It then travels at a constant speed for 15 seconds. It finally hits the brakes and stops in 0.66 seconds. a. What was the final velocity of the car after accelerating? [20 m/s] b. What is the acceleration during braking? [-30.3 m/s 2 ] c. What was the total distance traveled? [407 m]
29. A truck is traveling at 28 m/s for 17 seconds. The driver sees a deer and slams on the brakes and stops the truck in 53 m. a. How far did the truck travel (total)? [529 m] b. What is the acceleration during braking? [-7.4 m/s 2 ] c. How long did it take for the truck to stop? [3.79 s] 30. A physics student is traveling back home to get their physics book. They start from rest (at school) and accelerate at 1.5 m/s 2 for 2.0 s, they then travel at a constant speed for 10.0 s, finally, the decelerate to rest at -0.45 m/s 2 over a distance of 10.0 m. A. What is the total distance traveled? [43 m] B. What is the average velocity for the entire trip? [2.3 m/s]
VERTICAL MOTION PROBLEMS 31. What is the velocity of a dropped rock after it has fallen for 2.8 s? 32. What is the velocity of a dropped ball after it has fallen 11 m? [-27.4 m/s] [-14.7 m/s]
33. A ball is thrown straight up with a velocity of 14 m/s; what will be its velocity 2.0 s after being released? 34. A ball is thrown straight down with a velocity of 14 m/s; what will be its velocity 2.0 s after being released? [-5.6 m/s] [-33.6 m/s]
35. A ball is thrown straight up from the ground with an unknown velocity. It returns to the ground after 3.7 s. With what velocity did it leave the ground? [18.1 m/s] 36. A ball is thrown straight up from the ground with an unknown velocity. It reaches its highest point after 3.5s. With what velocity did it leave the ground? [34.3 m/s]
37. A ball is kicked upward from the ground at 18 m/s. a. How fast is it going when it is 11 m high?[±10.4 m/s] b. How long does it take to reach 11 m?[0.78 s and 2.9 s] c. Why are there two answers for a and b? 38. A baseball is hit and a fan observes it reaches its maximum height in 2.65 seconds. a. Calculate its initial velocity. [26 m/s] b. What is its maximum height? [34.4 m]
39. A balloon is rising at 5 m/s and is 40 m above the ground when a girl drops a sandbag. a. How much higher will the sandbag go? [1.28 m] b. What will be its velocity when it reaches the ground? [-28.4 m/s] c. How long will it spend in the air? [3.41 s] 40. A person throws a ball vertically from atop a 16 m tall building. What was the initial velocity of the ball (direction too!) if: a. It reaches the ground in 5.0 seconds? [up at 21.3 m/s] b. It reaches the ground in 1.0 seconds? [down at 11.1 m/s or -11.1 m/s]
41. A rock is dropped from a cliff that is 25.0 m high. How long will it take to reach the bottom? 42. A soccer ball is kicked straight up with a velocity of 8.0 m/s. A. How high will it go? B. How long will it take to reach its maximum height? C. How much time will it spend in the air? D. What is its velocity after 1.25 seconds? [2.26 s] A [3.3 m] B. [0.82 s] C. [1.6 s] D. [ - 4.3 m/s]
43. A raindrop falls off a roof and reaches the ground 1.30 seconds later. A. How fast is it traveling when it reaches the ground? B. How will your answer in part A differ if there is air resistance? C. How tall is the building from which it fell? A. [-12.7 m/s] C. [8.28 m] 44. A snowball is thrown straight down with a velocity of 4.5 m/s from a roof that is 15.0 m high. What will be its velocity when it hits the ground? [-17.7 m/s]
45. Observe: A v 0 = 6.5 m/s B 10. m C A. What is the velocity of the ball at point A? Point B? [A: 0 m/s B: -6.5 m/s] B. How long does it take to reach point A? Point B? [A. 0.66 s B: 1.33 s] C. What is its velocity at point C? [-15 m/s] D. How long does it take to reach point C? [2.2 s] 46. An arrow is shot upward and after 0.65 seconds its velocity is +12.0 m/s. How high will it go? (hint: get v 0 first!) [17.2 m]
47. A rock is dropped from atop a building. If it takes the rock to 2.50 seconds to reach the ground, how tall is the building? 48. A student throws a softball vertically upward at a speed of 12.0 m/s. A. How high will it go? B. How long will it be in the air? C. What will be its velocity at a height of 5.00 m? Why 2 answers? D. What will be the ball s speed after 2.00 seconds? [30.6 m] A. [7.35 m] B. [2.45 s] C. [±6.78 m/s] D. [-7.60 m/s]
49. A helicopter is rising at a velocity of 4.50 m/s. At a height of 25.0 m above the ground a passenger drops their camera out of the window. A. How high above the ground will the camera go? B. How long will it take to reach the ground? C. With what speed will it hit the ground? 50. Mr. Tracey is on call at a fire. A survivor falls into the safety net from 15.0 m in the air. A. How long will it take for the person to reach the net? B. How fast will the person be going when they hit it? C. If the net bends 1.0 m, what will be the deceleration of the survivor? How many g s is this? A. [26.0 m] B. [2.76 s] C. [-22.5 m/s] A. [1.75 s] B. [17.1 m/s] C. [147 m/s 2 ] [15 g s]
Conceptual questions: 1. What is zero at the maximum height? 2. When is Δy negative? 3. An object is observed to rise for 2.0 s. How long will it take to fall? 4. Indicate the sign (+ or -) of the following for a ball that is going UP: Δy v a t 5. Indicate the sign (+ or -) of the following for a ball that is going DOWN (not dropped): Δy v a t 6. A dart is thrown up at 5 m/s. What will be its velocity when it comes back down? 7. A ball is thrown up. On its way up its acceleration is. At its maximum height its acceleration is. On its way back down its acceleration is. 8. From a roof a ball is thrown up at v 0. An identical ball is thrown down at v 0. Which ball will be traveling faster when it reaches the ground? 9. From a roof a ball is thrown up at v 0. An identical ball is thrown down at v 0. Which ball will hit the ground first? 10. From a roof a ball is thrown up at v 0. An identical ball is thrown down at v 0. Which ball will travel the most distance? 11. From a roof a ball is thrown up at v 0. An identical ball is thrown down at v 0. Which ball will have the greater acceleration? 12. From a roof a ball is thrown up at v 0. An identical ball is thrown down at v 0. Which ball will be traveling faster when it reaches the ground? 13. Explain how air resistance will affect your answer to #6