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The Basic Idea

Free falling objects accelerate downward at a rate of approximately 10 m/s/s (or 9.8 m/s/s). This means that for every second of motion, the velocity value changes by -10 m/s. If the initial velocity is known, the velocity at every 1-second interval can be easily predicted.

There are three very similar versions of this question. Here is one of those versions.

​Version 1
A ball is projected upward with an initial speed of approximately 30 m/s. The diagram at the right represents its position at 1-second intervals of time. At what location will the ball be moving upward with a speed of approximately 10 m/s?

You will see a diagram with several lettered locations. You are given the speed at location A. You want to know at which location will the object be moving upward with a speed of 10 m/s. To do so, you need to know at least two things:

  1. A free-falling object accelerates downward with an acceleration of approximately -10 m/s/s. 
  2. The vertical velocity of the object is changing by -10 m/s for every second of motion.


The lettered dots on the diagram represent the location at 1-second intervals.  So beginning at location A (where the speed is known), go dot by dot through the diagram. Subtract 10 m/s each time you arrive at a new dot on the diagram until you get to 10 m/s. There will be two such locations - one on the first half of the trajectory and the other on the second half of the trajectory. Since the question states that the object is moving upward at 10 m/s, you will need to pick the first of these two points. The location on the upward side of the trajectory where the velocity becomes 10 m/s is the answer to this question.
 


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