Science 2201 Problem Set #1

Speed is the distance an object travels divided by the time that it takes to travel that distance.
  speed = distance / time
  S = d / t

Acceleration is the amount of change in velocity divided by the time it takes the change to occur.
  acceleration (m/s2) = [finial velocity – initial velocity (m/s)] / time (s)
  A = (vf-vi) / t

Velocity of a falling object is proportional to the length of time that it has been falling.

  velocity (m/s) = constant g (m/s2) x time (s)
  where g = 9.8 m/s2  (may be rounded to 10 m/s2) 
  v = g x t

Newton’s 2nd Law
The greater the force, the greater the acceleration; but the more massive the object being acted upon by the force, the smaller the acceleration.

  Force (newtons)  = mass (kg) x acceleration (m/s2)
  F = m x a

Work is equal to the force that is exerted times the distance over which it is exerted.

  Work (joules) = force (newtons) x distance (meters)
  W = F x d

1) What is the average speed of a cheetah that sprints (a) 100 m in 4 s? (b) 50 m in 2 s?

2) A car moved at an average speed of 60 km/hr for 1 h. (a) How far did it go? At this rate, how far would it go (b) in 4 h? (c) in 10 h?

3) During this 1-h trip, is it possible for the car to have an average speed of 60 km/h and never exceed a reading of 60 km/hr on the speedometer?

4) The speedometer of a car moving to the east reads 100 km/h. The car passes another car moving to the west at 100 km/h. Do both cars have the same speed? Do they have the same velocity?

5) During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? A constant velocity?

6) The ocean’s level is currently rising at a rate of about 1.5 mm per year. At this rate, in how many years will the level be 3 m (meters) higher than it is now?

7) A particular car can go from rest to 90 km/h in 10 s. What is its acceleration?

8) In 2.5 s, a car increases its speed from 60 km/h to 65 km/h while a bicycle goes from rest to 5 km/h. Which undergoes the greater acceleration? What is the acceleration of each?

9) What is the acceleration of a vehicle that changes its speed from 100 km/h to a dead stop in 10s?

10) If you could measure the velocity of a falling rock at particular time increments, what would its velocity be at 2 seconds, 3 seconds, 6 seconds, and 10 seconds after the rock drops from rest?

11) A cat steps off a ledge and drops to the ground in ½ second. 
a) What is its speed on striking the ground?
b) What is its average speed during the ½ s?
c) How high is the ledge above the ground?
     Use the approximate value of 10 m/s2 for g.

12) Charlie drove his car around the block at constant velocity? True or False? Explain.

13) Cedric says acceleration is how fast you go. Melissa says acceleration is how fast you get fast. They look to you for confirmation. Who’s correct?

14) For a freely falling object dropped from rest, what is its acceleration at the end of the fifth second of fall? The tenth second? Defend your answer.

15) Suppose a freely falling object were somehow equipped with a speedometer. By how much would its speed reading increase each second?

16) Suppose that a freely falling object were equipped with an odometer. Would the reading indicate equal or unequal distances covered in successive seconds? Explain.

17) A climber near the summit of a vertical cliff accidentally knocks loose a large rock. She sees it shatter at the bottom of the cliff 8 seconds later. What was the speed of impact? How far did the rock fall?

18) Acceleration has been defined as the time rate of change in velocity(a = change in velocity / time). By algebra we can rearrange Newton’s second law to say that acceleration is the ratio of force to mass a = F/m). Which is it? (Might both concepts hold true? Explain)

19) In an orbiting space shuttle, you are handed two identical boxes, one filled with sand and the other filled with feathers. How can you tell which is which without opening them?

20) Your empty hand is not hurt when it bangs lightly against a wall. Why is it hurt if it bangs the same wall while carrying a heavy load? Which of Newton’s laws is most applicable here?

21) A rocket becomes progressively easier to accelerate as it travels through space. Which of Newton’s laws is most applicable here?

22) A common saying goes, “It’s not the fall that hurts you; it’s the sudden stop.” Translate this into Newton’s laws of motion.

23) If a Mack truck and Honda Civic have a head-on collision, upon which vehicle is the impact force greater? Which vehicle undergoes the greater change in motion? Explain24) How much acceleration does a 747 jumbo jet of mass 30,000 kg experience in takeoff when the thrust for each of four engines is 30,000 N?

25) (a) How much work is done in lifting a 100 N box a vertical distance of 3 m? (b) How much work is done in pushing the same loaded box up a 6-m-long ramp? The force needed is only 50N (which is why inclines are useful tools).