1) Average speed is the total distance traveled divided by the time taken to cover the distance.

• We use the letters s for speed, d for distance, and t for time whence:

• sav = d/t.• The SI units of speed are

m/s.• Usain Bolt traveled 100 m in

9.63 s. What was his average speed?

2) A multi-exposure photograph is made in a totally dark room with a strobe and a camera with an open shutter.

• If you travel 40 miles in 2 hours your average speed is sav = 40 mi/2 h = 20 mi/h = 20 mph.

• Average speed tells you nothing about the details of the trip.

• What is happening to the speed of the blue ball?

3) Instantaneous speed is equal to the average speed over a time interval that is very, very small.

• For practical purposes we need a time interval that is small enough that the average speed does not change very much if we use an even smaller time interval.

• Think of instantaneous speed as what a speedometer says. How does it work?

4) Velocity is speed and direction. The magnitude of velocity is speed. Quantities that have both magnitude and direction are called vectors.

• Average velocity is displacement divided by time. vav = Dx/t.

• Displacement is a vector quantity whose magnitude is the straight-line distance from A to B and whose direction is the direction from A to B.

• Is the displacement vector ever longer than the distance traveled?

5) Average acceleration is the change in velocity divided by the time it takes to make that change.

• We use the letters a for acceleration, v for velocity, and t for time whence:

• aav = Dv/Dt.• The SI units of acceleration

are m/s2.• When you travel in a

straight line at a constant speed your acceleration is zero.

• The falling ball accelerates!

6) According to Aristotle, a heavy physics text should fall significantly faster than a crumpled piece of paper.

• According to Galileo, in a vacuum, the falling speeds of a cannonball and a feather should be equal.

• Astronauts conducted an ultramodern demonstration of this on the Moon where a hammer and a feather fell at the same rate.

• Why does the hammer fall faster on Earth?

7) As Galileo let balls roll down steeper ramps he discovered the following rule: the acceleration in each case is constant.

• Constant acceleration means the speed changes by the same amount each second.

• In the case of free fall the acceleration due to gravity is about 9.8 m/s2.

• We use the letter g for this acceleration and usually round it off whence:

• g = 10 m/s2.

8) If you throw a ball vertically upward with an initial speed of 20 m/s, one second later its instantaneous speed will be 10 m/s.

• As the ball continues to rise against gravity it continues to lose speed. It will reach its maximum height in 2 seconds.

• At that moment the instantaneous speed of the ball will be zero.

• Is the ball rising or falling?

Exercise 58

Exercise 60

Exercise 62

Exercise 64

Exercise 66

Exercise 68

Exercise 70

Exercise 72

Exercise 74

Exercise 76

Exercise 80