# Projectile acceleration and velocity relationship

### What are the kinematic formulas? (article) | Khan Academy

Of course, to describe motion we must deal with velocity and acceleration, . This equation defines the maximum height of a projectile and depends only on the. Apr 30, A projectile's motion can be described in terms of velocity, time and height. How to Calculate the Jump Height From Acceleration Solve this equation for t by isolating it on one side of the equation shown in the previous. Plotting projectile displacement, acceleration, and velocity About x squared for example, and.

Now let's hop in a roller coaster or engage in a similarly thrilling activity like downhill skiing, Formula One racing, or cycling in Manhattan traffic.

Acceleration is directed first one way, then another. You may even experience brief periods of weightlessness or inversion. These kinds of sensations generate intense mental activity, which is why we like doing them. They also sharpen us up and keep us focused during possibly life ending moments, which is why we evolved this sense in the first place.

Your ability to sense jerk is vital to your health and well being. Jerk is both exciting and necessary.

Constant jerk is easy to deal with mathematically. As a learning exercise, let's derive the equations of motion for constant jerk. You are welcome to try more complicated jerk problems if you wish.

Jerk is the derivative of acceleration. Integrate jerk to get acceleration. That's the first time I've ever said that. I propose we call this the zeroeth equation of motion for constant jerk. The reason why will be apparent after we finish the next derivation.

Old videos on projectile motion Video transcript What I want to do with this video is think about what happens to some type of projectile, maybe a ball or rock, if I were to throw it straight up into the air. To do that I want to plot distance relative to time. There are a few things I am going to tell you about my throwing the rock into the air.

The rock will have an initial velocity Vi of We also know the acceleration near the surface of the earth. We know the force of gravity near the surface of the earth is the mass of the object times the acceleration.

## What are the kinematic formulas?

The whole reason why I did this is when we look at the g it really comes from the universal law of gravitation.

You can really view g as measuring the gravitational field strength near the surface of the earth. Then that helps us figure out the force when you multiply mass times g. This is accelerating you towards the center of the earth. The other thing I want to make clear: You might be saying "Wait, clearly the force of gravity is dependent on the distance. So if I were to throw something up into the air, won't the distance change.

## Kinematics & Calculus

That is technically right, but the reality is that when you throw something up into the air that change in distance is so small relative to the distance between the object and the center of the earth that to make the math simple, When we are at or near the surface of the earth including in our atmosphere we can assume that it is constant.

Remember that little g over there is all of these terms combined. If we assume that mass one m1 is the mass of the earth, and r is the radius of the earth the distance from the center of the earth So you would be correct in thinking that it changes a little bit.

The force of gravity changes a little bit, but for the sake of throwing things up into our atmosphere we can assume that it is constant.

### Horizontal and Vertical Components of Velocity

And if we were to calculate it it is 9. I want to be clear these are vector quantities.

When we start throwing things up into the air the convention is if something is moving up it is given a positive value, and if it is moving down we give it a negative value. Well, for an object that is in free fall gravity would be accelerating it downwards, or the force of gravity is downwards.

• Deriving displacement as a function of time, acceleration, and initial velocity
• Describing Projectiles With Numbers: (Horizontal and Vertical Velocity)

So, little g over here, if you want to give it its direction, is negative. Little g is So, we have the acceleration due to gravity. The acceleration due to gravity ag is negative 9. Now I want to plot distance relative to time.