To find the velocity and acceleration when the height is given and the mass is constant, we need to use the principles of physics, specifically those related to motion under gravity. Let's break down the process step by step:
Start with the given information: the height (let's call it h) and the constant mass (let's call it m).
Determine the potential energy at the given height. The potential energy (PE) of an object at a certain height is given by the equation PE = mgh, where g is the acceleration due to gravity (approximately 9.8 m/s²).
Convert the potential energy into kinetic energy. When the object is at the given height, all of its potential energy will be converted into kinetic energy. The equation for kinetic energy (KE) is KE = (1/2)mv², where v is the velocity of the object.
Equate the potential energy and kinetic energy equations: PE = KE. This gives us mgh = (1/2)mv².
Cancel out the mass (m) from both sides of the equation: gh = (1/2)v².
Solve for velocity (v): Multiply both sides of the equation by 2 and then take the square root to isolate v. The equation becomes v = √(2gh).
Calculate the velocity using the equation v = √(2gh), substituting the known values for g and h.
Once you have the velocity, you can also calculate the acceleration (a). Since the mass is constant, the acceleration will be due solely to gravity, and its value will be equal to the acceleration due to gravity (g). Thus, the acceleration will be approximately 9.8 m/s².
By following these steps, you can find the velocity and acceleration when the height and mass are given, assuming the only force acting on the object is gravity.