This chapter has presented many of the commonly used equations for analyzing motion, but more of them can be derived. In this section, we challenge you to derive an equation that is required to solve the problem we pose. You can test its validity in the simulation to the right.

Your spacecraft is collecting the mail from a planet. The mail is fired up from the planet and you pick it up when it has reached its maximum distance from the planet. The mail will be there in 9.00 seconds. Your craft starts 6.00 kilometers from the pickup point. You fire retrorockets to slow down your spacecraft, but alas, your velocity gauge is broken, so you do not know your current velocity. Your spacecraft must have zero velocity when it reaches the mail.

In sum, you know the final desired velocity (zero), the displacement and the time. You set the acceleration to slow the rocket down. If you can develop a motion equation that does not require the initial velocity but includes these other factors, then you can determine what the acceleration should be. Enter the acceleration to the nearest meter per second squared (e.g., 178 m/s²), then press GO. Press RESET to try again.

For an additional challenge, determine the rate of free-fall acceleration experienced by the mail package. The rate of acceleration is constant, but since the planet in the simulation is not Earth, it does not equal g.