Speedy Science: How Does Constant Acceleration Affect Distances Traveled?
Summary
Introduction
Have you ever dropped something and wondered how fast it was moving while falling? If it was something fragile, like a cell phone, you might not have been thinking about this at the time – you were likely too busy trying to grab the phone! But you probably wanted to find out how hard it hit the ground afterwards. We all know that gravity forces an object to fall, but how does this affect how quickly something falls and its impact? For example, did the phone move faster right after leaving your hand, or just before hitting the ground? In this science activity, you’ll explore the relation between time and distance traveled when a moving object is under gravity’s constant acceleration.
Background
You know from experience that when you ride a bike downhill, it’s easy to go fast. Gravity helps pull you down, so you don’t have to do all of the work with the pedals. You also know from experience that the longer the hill, the faster you go. The longer you feel that pull from gravity, the faster it makes you go. Finally, you also know that the steeper the hill, the faster you go. The maximum steepness is a sheer vertical drop – when objects go into free fall, and when gravity gives the biggest pull of all. You wouldn’t want to try that on your bicycle!
In free fall, gravity constantly accelerates an object (increases its velocity). Specifically, gravity increases a falling object’s velocity by 9.8 meters per second (m/s) with every passing second. (While velocity is measured in m/s, acceleration is measured in meters per second squared [m/s2].) How does this constant acceleration affect the distance that an object travels over time? In this science activity, you’ll roll a marble down a ramp to find out!
Materials
- Long cardboard tube, such as an empty roll of wrapping paper, to make your ramp. It should be at least 2 ½ feet long.
- A thin book or small wood block to raise one end of your ramp. It should be about ½ inch to one inch in thickness.
- Pair of scissors for cutting the cardboard tube
- Permanent marker
- Marble
- Timer. Make sure it can accurately count individual seconds. Many cell phones have a timer that is this accurate.
- A ruler (optional)
- A helper (optional)
Preparation
- Take a long cardboard tube and cut it straight along one of its (long) sides. Then cut it along the other side so that you end up with two long pieces that are each semicircles. You will use one of these pieces as the ramp for the marble.
- Take one of the semicircle pieces you just cut and raise one end slightly by placing it on a thin book or small block (no thicker than one inch). (You want a low slope so that the marble does not roll too fast to measure.)
- Use the permanent marker to mark a starting line across the high end of the ramp, about ½ inch from the end. You ramp is now ready for some marble-rolling action!
Instructions
- Set the timer for one second and then hold a marble in place at the starting line.
- At the exact same time, release the marble (being careful not to give it a push as you let it go) and start the timer. If you have a helper, have them watch the marble for you. Use the permanent marker to mark where the marble was one second after releasing it. How far did the marble travel?
- Repeat this process at least nine more times. This means you should end up with at least ten different marks on the ramp, showing where the marble was one second after releasing it each time. Did the marble travel similar distances each time?
- Repeat this process but this time mark where the marble is at two seconds after releasing it. Do this at least ten times, so you’ve made at least ten more marks on the ramp. How does the distance the marble traveled after one second compare to the distance it traveled after two seconds? Specifically, how does the distance between the starting line and the one-second marks compare to the distance between the one-second marks and the two-second marks?
- If you have a ruler, you can measure the distance the marble rolled each time from the starting line.
- Overall, how did the distance the marble traveled change as it rolled down the ramp for a longer amount of time? What does this tell you about the effect of gravity on the velocity and acceleration of the marble as it rolled?
Extra: Use a ruler to measure the marks you made on the ramp and calculate the average distance the marble traveled for one second and for two seconds (averaging the times separately). Then graph your results, putting the average distance traveled on one axis and the time on the other axis. Based on your graph, how did the distance the marble traveled change as it rolled for a longer amount of time?
Extra: Try repeating this activity using a longer ramp, such as a flat board that is at least six feet long (with a groove down the middle, or another straight piece of wood glued along the length of the first board to act as a guide). Roll the marble down the longer ramp for increasing amounts of time (i.e., one second, two seconds, three seconds, etc.) until the time the marble goes past the end of the ramp. Mark the distance traveled on the ramp each time. Using a longer ramp, how does gravity appear to affect the velocity and acceleration of a marble as it rolls downhill?
Extra: Try repeating this activity with different balls, such as a rubber ball, large metal ball, ping pong ball, etc. How does the type of ball affect how it travels down the ramp?
Observations and Results
Did the marble travel faster as it went down the slope?
When an object is in free fall, gravity increases its velocity by 9.8 m/s with every passing second. So after one second, the object would be falling at a velocity of 9.8 m/s. After two seconds, the object would be falling at a velocity of 19.6 m/s. After three seconds, the object would be falling at a velocity of 29.4 m/s, and so on.
Gravity should have also constantly accelerated the marble as it rolled down the ramp in this activity. This can be seen by comparing the (average) distance between the starting line and the one-second marks to the distance between the one-second marks and the two-second marks. Specifically, the distance between the one- and two-second marks should have been greater than the distance between the starting line and the one-second marks, showing that the marble was moving faster the longer it rolled. Depending on the exact conditions of your ramp setup, the distance between the one- and two-second marks may have been about 1.5 to 2.5 times the distance between the starting line and one-second marks.
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Additional Resources
- Inclined Planes, from the Physics Classroom
- Acceleration, from the University of California at Berkeley
- Science Activities for All Ages!, from Science Buddies
- Distance and Constant Acceleration, from Science Buddies
