If a freely falling rock were equipped with a speedometer, by how much would its speed readings increase with each second IF it were on a planet where g = 20 m/s2? Show all work leading to your answer.
To determine the increase in speed of a freely falling rock on a planet with a gravitational acceleration (g) of 20 m/s², we can use the equation for free fall:
V = gt
where V is the velocity/speed, g is the acceleration due to gravity, and t is the time.
In this case, we want to determine the increase in speed per second, so we need to find the difference in velocity between one second and the next.
Let's calculate the speed at t = 1 second:
V₁ = g * t
V₁ = 20 m/s² * 1 s
V₁ = 20 m/s
Now let's calculate the speed at t = 2 seconds:
V₂ = g * t
V₂ = 20 m/s² * 2 s
V₂ = 40 m/s
The increase in speed per second is the difference between V₂ and V₁:
∆V = V₂ - V₁
∆V = 40 m/s - 20 m/s
∆V = 20 m/s
Therefore, on a planet where gravity is 20 m/s², the speed readings of the rock would increase by 20 m/s with each second of free fall.