Gravity and acceleration

  • Under the influence of Earth's gravity, heavy and light objects fall the same way[*]. ("Ball and feather" video as well as your experiments)
  • As objects fall, their speed changes, but their acceleration remains constant[*]. (Your experiments)
  • "Near" Earth's surface, that constant acceleration is approximately 9.8 m/s/s. (See any physics textbook.) Your class average of $g$=9.6$\pm$0.6 m/s/s agrees with this value, to within experimental uncertainty.
  • [*] As long as we don't have to worry about air resistance.

    What does it mean that your class $g$ agreed with 9.8 m/s/s in terms of the air resistance? Did we have no air? What do you guess that air resistance depends on?

Some problems to work with gravity

$$\text{acceleration}=g=9.8\text{ m/s/s} = \frac{\Delta v}{\Delta t}$$

For many problems, 9.8 m/s/s is very little different from 10 m/s/s! Use $g=$10 m/s/s in the following problems:

  1. A ball is released from rest and drops straight down. How fast is it moving 3 seconds later?

  2. A ball is released from rest and drops straight down. How fast is it moving 5 seconds later?

  3. Come up with a formula for the speed, $v(t)=?$, at $t$ seconds after you drop a ball from rest.
  4. A ball is thrown upwards with a starting speed of 10 m/s. What is its speed 3 seconds later?

  5. Can you modify your formula to take into account the initial speed of the ball?
  6. A ball is released from rest. How long (in seconds) until it's moving with a speed of 50 m/s?




  7. A ball is released from rest. How fast is it moving in feet per second 3 seconds later? (There are 12 inches in one foot, and there are 2.54 cm in one inch.)

  8. A ball is released from rest. How fast is it moving in miles per hour 3 seconds later?

  9. What is $g$ expressed in miles/hour/sec? (You may google that unit conversion!)
  10. A human being is released from rest. Assuming that you can neglect air resistance, how long will it take him/her to reach the speed of sound ("Mach 1")? Mach 1 = 340 m/s (=760 mph = 1225 km/h).

    See: Felix Baumgartner steps off at 120,000 feet, and the view from Felix' helmet cam (with stats)



  1. Is Felix "weightless" while falling?
  2. Is gravity acting on Felix while he's dropping?
  3. Why does Felix stop accelerating after a while?
  4. According to Newton, $a=F/m$, so $F=0$ means that $a=0$. Is gravity no longer acting on Felix when his speed is constant?
  5. What forces besides gravity are acting on Felix?

High speed vs low speed

Air resistance increases the faster you go.

Or

The slower you go, air resistance becomes less important.

Stop and go traffic

In town, vehicles may spend most of their time at speeds less than 30 mph. Stop signs / traffic lights are frequent. Air resistance is not terribly important. The force from the engine (and eventually energy) is mostly used to accelerate from a stop. $$a=\frac fm.$$

Highways / cruising


On the highway, speed is constant. Speeds are high. The force from the engine (and eventually energy) is used to overcome air resistance (and to a lesser degree, rolling resistance).