3 level problems: v = d/t
Level 1: Numbers only
v / d / t20m / 30s
8.5km / 2.13h
30.1 m/s / 20s
152 km/h / 1 hour and 30 min
85 m/s / 9.1 h
23.8 m/s / 8.15 m
3.19 m/s / 9.27 m
87.3 m/s / 71.3m
9.25 m/s / 18.75 km
Level 2: word problems
1. A bicycle travels 18 km in 15 min. What is the velocity in m/s?
2. A frog hops 1 m in ¾ minute. What is the velocity in m/s?
3. A car travels at 55 km/h for 17 minutes. What distance did the car cover?
4. Light from the sun reaches the earth in 8.3 minutes. The speed of light is 3.00 x 108 m/s. How far is the earth from the sun?
5. A horse gallops at the constant rate of 102.7 m/s. How far does the horse go in 3 minutes?
6. Saturn is 7.5 x 104 miles wide. Traveling at the speed of light, how long does it take to travel from one side to the other?
Level 3: multiple step word problems
7. At a recent regatta in California, The San Diego Crew Classic, results from the Men's Cal-Visitors Cup Grand Final with their times are as follows:
The course is 2000m long. Assuming constant velocity for all boats, how far behind OSU was each boat when OSU crossed the finish line?
8. Donovan Bailey of Canada broke the world record in the 100m dash at the 1996 Atlanta Olympics with a time of 9.84 seconds. With this gold medal, he became "the world's fastest man"
a.
What was his average velocity over this distance in meters per second and miles per hour?
b.
A couple of days later, Michael Johnson set the world record in the 200m dash with a time of 19.32 seconds. What was his average speed?
c.
Is Donovan Bailey the world's fastest man?
3 level problems a = dv/dt
Level 1: numbers only
a / Vf / Vi / Δv / Δt1 / 0.278 m/s / 0 m/s / 1800 s
2 / 0 / 0.417 m/s / 900 s
3 / 1.7 km/h / 0 / 1 h
4 / 0.0139 m/s2 / XXXXXXX / XXXXXXX / m/s / 15 min
5 / 0.0112 m/s2 / XXXXXXX / XXXXXXX / m/s / 0.35 h
6 / 9.54 m/s2 / XXXXXXX / XXXXXXX / m/s / 0.55h
7 / 3.67 m/s2 / 15.2 m/s / 0 m/s / s
8 / 2.5 km/h2 / 0 / 8.37 km/h / h
9 / 6.51 km/min2 / 0 / 21.7 km/s / min
Level 2: word problems
1. A lioness is walking sluggishly across a savannah at a constant rate of 15.7 km/h. She sees an elephant that is 72m away. The lioness speeds up to 72.7 km/h within 28s. What is the lioness’ acceleration in m/s2?
2. A garden snail sleeps soundly under a daffodil. When he awakens, he travels at a constant velocity of 4.83 x 10-2 km/h for 5.2 min and reaches a can. What is the snail’s acceleration?
3. A car traveling down Hooks Mill Road at a constant velocity of 60mil/h has come to a complete stop within 27s. What is the car’s acceleration in m/s2?
4. A train is accelerating at the rate of 1.57 m/s2. Starting from rest, the train will reach full speed in 2.5 min. What is the train’s speed at that time?
5. At an accident scene, police measure skid marks from a car to be 17.2 m. The car was traveling at a constant velocity until the driver sneezed and noticed a cement barrier directly in front of him. From the time the driver sneezed until he hit the barrier, 0.7s had passed. What was the driver’s velocity before he sneezed if his rate of acceleration was -8.2m/s2?
6. How long (in s) will it take for Sue to reach a speed of 55 miles/h as she moves from the 45 mile/h zone? Her constant acceleration from 45 mil/h to 55 mil/h is 87 mil/h2.
7. A pelgrin falcon sitting on a power line sees a rodent on the ground. The pelgrin falcon is capable of flying 322 km/h. After studying his prey, he flies into action. At an acceleration of 1.5 x 104 km/h2, it takes him 2 seconds to reach his prey. Does the falcon reach his maximum velocity?
8. The acceleration on Earth due to gravity is 9.8m/s2. If an egg falls off of a counter, what is its velocity as it hits the floor 0.5s later?
9. A train accelerating at -7200 km/h2 comes to a complete stop after traveling at a constant rate of 235 km/h. How many minutes does it take the train to stop?
Level 3
10. A boat travels 272 m in 25s at a constant velocity. The boat accelerates to 11.5m/s in 10. s. What is the boat’s average acceleration?
3 level problems for equations:
,
df / di / Δd / vf / vi / Δv / t / a1 / X / X / X / X / X / 3.1s / 7.2m/s2
2 / X / X / X / X / X / 0.57s / -1.5m/s2
3 / X / X / X / X / X / 2.3min / 2.5m/s2
4 / X / X / X / 5.45m/s / 5s / 0.9m/s2
5 / X / X / X / 0 / 0.5s / -6.5m/s2
6 / X / X / X / 500km/s / 2.2min / 1.7km/s2
7 / X / X / X / 0 / 1.33min / -0.31m/s2
8 / X / X / X / 0.9m/s / X / 3s / 5.1m/s2
9 / X / X / X / 1.3m/s / X / 6s / 0.8m/s2
10 / X / X / X / 17.2km/h / X / 15s / 27.5km/h2
11 / X / X / 32m / X / X / 5s / -2.8m/s2
12 / X / X / 185m / X / X / 2.1s / 8.37m/s2
13 / X / X / 93.8m / X / X / 4.1s / -38.5m/s2
14 / X / X / 12m / X / 5m/s / X / 12s
15 / 63m / 26m / X / 18m/s / X / 0.8s
16 / X / X / 0.5km / 200.52km/h / X / 4min
17 / X / X / 15m / 27m/s / X / X / 5m/s2
18 / X / X / 48m / 9.8m/s / X / X / -8.5m/s2
19 / X / X / 4.3m / 0 / X / X / -16m/s2
20 / X / X / 90km / 120km/h / X / X / 50km/h2
Level 2
1. A golf ball rolls up a hill toward a miniature golf hole. Assume that the direction toward the hole is positive.
a. If the golf ball starts with a speed of 2.0m/s and slows at a constant rate of 0.50m/s2 what is the velocity after 2s?
b. What is the golf ball’s velocity if the constant acceleration continues for 6.0s?
2. A bus that is traveling at 30.0km/h speeds up at a constant rate of 3.5m/s2. What is the velocity 6.8s later?
3. A car slows from 22m/s to 3.0m/s at a constant rate of 2.1m/s2. How many seconds are required before the car is traveling at 3.0m/s?
4. A race car travels on a racetrack at 44 m/s and slows at a constant rate to a velocity of 22m/s over 11s. How far does it move during this time?
5. A car accelerates at a constant rate from 15m/s to 25m/s while it travels a distance of 125m. How long does it take to achieve this speed?
6. A bike rider pedals with constant acceleration to reach a velocity of 7.5m/s over a time of 4.5s. During the period of acceleration, the bike’s displacement is 19m. What is the initial velocity of the bike?
7. A man runs at a velocity of 4.5m/s for 15.0 min. When going up an increasingly steep hill, he slows down at a constant rate of 0.05m/s2 for 90.0s and comes to a stop. How far did he run?
8. You start your bicycle ride at the top of a hill. You coast down the hill at a constant acceleration of 2.00 m/s2. When you get to the bottom of the hill, you are moving at 18.0m/s, and you pedal to maintain that speed. If you continue at this speed for 1.00 min, how far will you have gone from the time you left the hilltop?
9. A woman driving at a speed of 23 m/s sees a deer on the road ahead and applies the brakes when she is 210m from the deer. If the deer does not move and the car stops right before it hits the deer, what is the acceleration provided by the car’s brakes?
10. An in line skater first accelerates from 0.0 m/s to 5.0m/s in 4.5s, then continues at this constant speed for another 4.5s. What is the total distance traveled?
11. A plane travels a distance of 5.0x102m while being accelerated uniformly from rest at the rate of 5.0m/s2. What final velocity did it attain?
12. An airplane starts from rest and accelerates at a constant 3.00m/s2 for 30.0s before leaving the ground.
a. How far did it move?
b. How fast was the airplane going when it took off?
Level 3
1.The driver of a car going 90.0 km/h suddenly sees the lights of a barrier 40.0m ahead. It takes the driver 0.75s to apply the brakes, and the average acceleration during braking is -10.0m/s2.
a. Determine whether the car hits the barrier.
b. What is the maximum speed at which the car could be moving and not hit the barrier 40.0m ahead? Assume that the acceleration does not change.
2. A helicopter is rising at 5.0m/s when a bag of its cargo is dropped. The bag falls for 2.0s.
a. What is the bag’s velocity? (acceleration due to gravity is 9.80m/s2)
b. How far has the bag fallen?
c. How far below the helicopter is the bag?