Distance, Velocity and Time: Equations and Relationship (page 2)

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Author: Beth Touchette


Your results are likely to be pretty close to what your graph predicts, but they will likely vary depending on the velocities of your cars and whether or not they travel at a consistent velocity. Conduct more trials if you wish. If your graph still doesn’t match your actual results, you might want to re-measure the velocity of both your cars again and redraw your graph.


Uniform velocity is a linear function, making them easy (and fun) to predict. The steeper the slope of each function’s line, the faster the car each line represents. Although the slower car had a head start in distance, the faster car covered more distance in less time, so it caught up. This is where the lines crossed.

A non-graphical way of looking at this is using the following equation: d=d0 + vs(t-t0) where

  • d is the total distance
  • t is the total time
  • d0  is the head start distance
  • vs is the slower car’s velocity, and
  • t0is the time in seconds for the head start.

The equation for the fast car is d= vf (t), where vis the velocity of the fast car. The total distance each car travels to intersect is the same. So, if the hare had measured his hopping velocity and the tortoise’s plodding velocity, and the total race distance, he could have figured out how much of a head start he could have given the tortoise and still won.

Going Further

The next time you’re about to say “Are we there yet?” on a long car trip with your parents, ask them what the car’s velocity and trip distance is instead. Then, you can tell your parents how soon you will arrive at your destination.

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