You can treat units just like you treat numbers, so a km/km=1 (or, we say, it cancels out). If we add them together, we see that the net displacement for the whole trip is 0 km, which it should be because we started and ended at the same place. If we calculate the same for the return trip, we get –5 km. The units for minutes cancel each other, and we get 5 km, which is the displacement for the trip to school. Let’s take just the first half of the motion. In Figure 2.16, we have velocity on the y-axis and time along the x-axis. If we use a little algebra to re-arrange the equation, we see that d = v × × t. time graph to determine velocity, we can use a velocity vs. There are a few other interesting things to note. Second, if we have a straight-line position–time graph that is positively or negatively sloped, it will yield a horizontal velocity graph.
First, we can derive a v versus t graph from a d versus t graph. Explain why displacement is a vector quantity.Figure 2.16 Graph of velocity versus time for the drive to and from school. Can you explain why Pythagoras’ Theorem can be used to find the calculated displacement in your last walk? Hint: you made a 90 degree turn on your walk. Label the square of each leg of your triangle on the diagram. Show with the same diagram how you used Pythagoras’ theorem to find your calculated displacement. Show all your measured distances and displacements on the diagram. Now diagram the last walk and indicate displacement with a vector arrow. Does it match your measured displacement (or nearly so)? 17. This value is your calculated displacement. If you have a calculator, find the square root of the value you found for the sum of the square of #13 and square of #14. Write it here: _The two numbers should be equal or nearly so. Write it here:_ Now square the distance you measured in number 15 (your measured displacement). You can use Pythagoras’ Theorem! Add the square of number 13 and the square of number 14. Distance = _ Here’s a way to figure out your calculated displacement. Now figure out your distance and write it below. Have your partner measure how far you are from the origin, your measured displacement, and write it here: _ (Turn this page over and continue.) 16. Measure how far you walked and write it here: _ 15. Measure how far you walked and write it here: _ 14. Find your piece of tape again, and walk 20 steps forward. Calculated Displacement = _ Does your calculated displacement match your measured displacement? _ 13. Add number 7 + number 8 then subtract number 9 and number 10.
Distance = _ Now figure out your calculated displacement and write it below. Add up the measurements you wrote in numbers 7 through 10. Write it here: _ This is your measured displacement. Have your partner measure how far you are form the origin. Turn 90° left, walk 20 steps and measure how far you walked. Turn 90° left, walk 10 steps and measure how far you walked. Turn 90° left, walk 15 steps and measure how far you walked. Write it here: _ (don’t forget your units!) 8. Find your piece of tape again, and walk 10 steps forward and measure how far you walked. Add all measurements to find the distance: _ Add all forward measurements and subtract all backwards measurements to find the calculated displacement: _ Did your measured displacement match your calculated displacement? _ 7. Figure out the distance and calculated displacement you walked. Write that measurement here: _ This is your measured displacement. Finally, have your partner measure how far you are from the origin. Write that distance here: _ (don’t forget units!) 5.
Using the meter stick, have your partner measure the distance you walked. Now turn 180 degrees and walk 20 steps and stop. Write that distance here: _ (don’t forget units!) 4. Now turn 180 degrees and walk 5 steps and stop. Write that distance here: _ (don’t forget units!) 3. Place a piece of tape where you will begin your walk outside. Distance and Displacement Lab Note! In this lab when you measure, round all measurements to the nearest meter! 1.