you're conducting a physics experiment on another planet. you drop a rock from a height of 2.1 m and it hits the ground 0.6 seconds later. what is the acceleration due to gravity on this planet?
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s = 1/2 a t^2
solve for a
The brief explanation for the above equation is that, since acceleration is expressed as m/s^2 and time squared as s^2, the time units cancel each other out. As for 1/2, you need to use 1/2 because you are multiplying 2 values in respect to per unit of time, and it would be illogical to assume that one would get an answer by multiplying 2 values over the same unit.
Many people mechanically use the kinematics equation without understanding the reasons behind them. It is empirical that you know what each of the equation means so that you can apply them when introduced with questions different from the scenarios you learned the equations with.