Understanding Velocity and Gravity in Basic Physics Equations

[The_ArtofScience]

Hi

I am about to take Intro Physics this fall and I would like to get a few "what ifs" out of my mind. For starters, I have never been exposed to physics in hs (i choose the adv bio) so please be gentle

When an object of any sort attains a certain height gravity will pull the object down and height h= 1/2 gt^2. Velocity at some time t is = (v*sin$)/g and when its replaced back into the eq it becomes (v*sin$)^2/2g. Right? But when I draw a semicircle and label (x,y) on the x-axis how does it "become" v^2sin(2$)/g?

I saw in a book the other day that the average of velocity can be calculated as follows: v_f^2-v_0^2 =2gs. Where does the v^2=2gs terms come from? I notice that when you flip things around you get s = v^2/2g which looks a little similar to t in f(t) for maximum height

Thanks

 

[Doc Al]

When an object of any sort attains a certain height gravity will pull the object down and height h= 1/2 gt^2. Velocity at some time t is = (v*sin$)/g and when its replaced back into the eq it becomes (v*sin$)^2/2g. Right? But when I draw a semicircle and label (x,y) on the x-axis how does it "become" v^2sin(2$)/g?

Sounds like you are trying to derive the formula for the horizontal range of a projectile. Combine these two ideas: (1) The time of flight depends on the vertical component of initial speed; (2) The horizontal distance depends on the horizontal component of the initial speed.

To actually do this, you'll need to understand how to compute those quantities using the basic principles of kinematics.

I saw in a book the other day that the average of velocity can be calculated as follows: v_f^2-v_0^2 =2gs. Where does the v^2=2gs terms come from? I notice that when you flip things around you get s = v^2/2g which looks a little similar to t in f(t) for maximum height

That's not a formula for calculating average velocity. It's a kinematic relationship connecting velocity, distance, and acceleration.

Learn more about kinematic relationships here: http://hyperphysics.phy-astr.gsu.edu/Hbase/mot.html#mot1".

 

[baba89]

for your question and interest in understanding velocity and gravity in basic physics equations. I will do my best to explain these concepts in a clear and gentle manner.

First, it is important to understand that velocity is a measure of an object's speed and direction, while gravity is a force that pulls objects towards the center of the Earth. In basic physics equations, velocity is often represented by the letter v and gravity by the letter g.

Let's start with the first equation you mentioned, h=1/2 gt^2. This equation is known as the position equation and it calculates the height (h) of an object at a certain time (t) when it is thrown or dropped from a certain initial height. The g in this equation represents the acceleration due to gravity, which is approximately 9.8 meters per second squared on Earth. This means that for every second an object falls, its velocity increases by 9.8 meters per second.

Now, when you mention the equation for velocity at a certain time, (v*sin$)/g, it is important to clarify that the $ symbol represents an angle. In this case, it is the angle at which the object is moving. This equation is known as the velocity equation and it calculates the velocity (v) of an object at a certain time (t) when it is thrown or dropped from a certain initial height. When you plug this velocity equation into the position equation, you get (v*sin$)^2/2g. This is because velocity is the rate of change of an object's position, so you are essentially substituting the velocity equation into the position equation.

Moving on to the semicircle and the equation v^2sin(2$)/g, this equation is known as the range equation and it calculates the horizontal distance an object travels (x) when it is thrown or dropped at a certain angle ($). This equation is derived from the velocity equation (v*sin$)/g by multiplying it by time (t) and then substituting for t using t=2v*sin$/g. This gives us the range equation: x=v^2sin(2$)/g.

Finally, you mentioned the equation for average velocity, v_f^2-v_0^2=2gs. This equation is known as the average velocity equation and it calculates the average velocity of an object over a certain distance (s). The v_f and v_0 represent the final and initial velocities of the