Megafun Kinematics Worksheet

Problem Solving Suggestions:

o Identify an initial and a final instant

o Draw a picture showing both initial and final instants

o Label given information and unknown information

o Write down appropriate equations

o Find a way to solve for unknowns

1. You are standing on a street corner. An egg falls past and splats on the street. Being an expert in egg disintegration you estimate it was traveling 22 m/s when it hit. You assume the egg was dropped. (a) What amount of time did the egg fall? (b) From what height was it dropped? (c) Could the egg be scrambled and eaten?

2. Wyle E. Coyote is chasing the Roadrunner with velocity 15.0 m/s, 0° when he unwittingly runs into the Acme Giant Rubber Band that he previously had stretched across the road. The rubber band causes him to accelerate uniformly at 3.50 m/s², 180° until he is thrown back in the opposite direction. (a) What amount of time will he be in contact with the rubber band? (b) What velocity will he have as he leaves the rubber band? (c) What is the maximum amount the rubber band is stretched?

3. A motorcyclist traveling 35.0 m/s, 0° realizes suddenly that he is headed straight for the edge of the Grand Canyon 50.0 m away. He immediately begins to brake, decreasing his speed 7.00 m/s². With what velocity will he fly off into the canyon?

4. Starting from rest, Mr. M's bus achieves a velocity of 25 m/s, 180.0° in a distance of
1.0 km. Find the time and the acceleration.

5. A disgusted physics student wads up her homework and throws it downward into a trash can. If the wadded up paper takes 0.30 seconds to travel the 1.5 m from her hand to the bottom of the waste can, with what speed was the homework hurled? (What assumption must you make?)

6. Suppose this dude wants to be able to touch the rim of a basketball goal. The rim is 3.048 m above the ground. The dude can reach up 2.45 m with his feet on the ground. (a) If the dude can achieve a liftoff speed of 2.80 m/s, what is his maximum upward displacement?
(b) What is the closest to the rim his fingertips will get? (c) What would be the minimum liftoff speed necessary for this dude to touch the rim?

7. A hackey sack leaves a Converse high-top with velocity 10.0 m/s, 90.0°. At that very instant the sack is 50.0 cm above an old wad of gum on the floor. Use the gum as a reference. At a point in time 1.50 s later find the sack's: (a) velocity, (b) displacement, (c) position, and (d) flight distance.

8. A bungee jumping mime is attached to a bungee cord 25.0 m long. The mime is in freefall until he gets to the end of the bungee (25.0 m below starting point). Once the bungee begins to stretch, the mime's speed decreases. Assume the bungee cord causes the mime to accelerate at a constant 15.0 m/s², 90.0°. (a) Find the maximum speed attained by the mime. (b) Find the distance the mime falls before coming to a stop. (This distance could be used to decide how tall a tower to drop the mime from.)

9. A driving instructor tells his student to maintain a 2.00 second separation between the student's car and the car ahead. Suppose the cars are traveling 25.0 m/s. (a) How many meters apart are the cars? (b) If the trailing car brakes at 10.0 m/s² how much distance is required to stop? (c) Repeat (a) and (b) for two cars traveling at 50.0 m/s. (d) At what speed would the 2.00 s separation give just enough distance for stopping?

Use this graph to work problem 10.

10. The preceding graph depicts the motion of a fan cart moving along a level track. (This graph is actual data collected with a sonic ranging device. The cart was affected by the fan and also attached to an elastic cord so that it did a horizontal “bungee jump”.) (a) Determine the displacement of the cart during the 4 seconds shown. (b) Determine the distance traveled by the cart during the 4 seconds shown. (c) Determine the average velocity. (d) Determine the average speed. (e) Determine the velocity at t = 1.00 s. (f) Determine the speed at t = 1.00 s. (g) Determine the maximum speed of the cart during the 4 seconds shown. (h) At what point(s) in time was the cart’s speed zero? (i) All of the data shown on the graph displays a nonlinear pattern. What does this indicate about the motion of the cart (as opposed to what a linear pattern would indicate)?

Use this graph to work problem 11.

11. The preceding graph depicts the motion of a fan cart moving along a level track. (a) Is this graph consistent with the graph from problem 10? In other words, is this the velocity of the cart whose position was shown in the previous graph? Compare your speeds and velocities found in the problem 10. (b) During what interval(s) of time is the cart’s speed decreasing? (c) At what point(s) in time does the cart reverse direction? (d) Is there evidence of constant acceleration? If so what and where on the graph? (e) Draw a line of best fit for the data between t = 0.2 s and t = 1.4 s and use it to determine acceleration.
(f) Determine the cart’s acceleration when the velocity first reaches zero. Would it be fair to say this is the maximum acceleration shown? Why? (g) Determine the displacement of the cart from t = 2.40 s to t = 3.00 s. Compare to the position graph.

Answers

1. a. 2.2 s
b. 24 m
c. Perhaps, with the proper pan

2. a. 8.57 s
b. 15.0 m/s, 180.0°
c. 32.1 m

3. 22.9 m/s, 0°

4. t = 80 s, a = 0.31 m/s², 180°

5. 3.53 m/s (assuming no air resistance)

6. a. 0.400 m, 90.0°
b. 19.8 cm
c. 3.42 m/s

7. a. 4.7 m/s, 270.0°
b. 3.98 m, 90.0°
c. 4.48 m, 90.0° from the gum
d. 6.23 m

8. a. 22.1 m/s
b. 41.3 m (Perhaps a tower 30 m tall)

9. a. 50.0 m
b. 31.3 m
c. 100 m between, 125 m to stop
d. 40.0 m/s

10. a. 0.71 m, W
b. 2.0 m
c. 0.18 m/s, W
d. 0.50 m/s
e. 0.80 m/s, W
f. 0.80 m/s
g. 1.15 m/s
h. t = 1.98 s and t = 3.30 s
i. The nonlinear graph shows that the cart’s velocity was constantly changing.

11. a. Yes, this graph shows the velocity of the object depicted in the position graph.
b. 1.56 s < t <1.98 s and 2.36 s < t < 3.30 s
c. t = 1.98 s and t = 3.30 s
d. Wherever the graph is linear the cart had constant acceleration.
e. 0.78 m/s², W
f. 3.5 m/s², E appears to be maximum because it is the greatest slope shown
g. 0.36 m, E