# Equations of Kinematics, including gravity

• Runner1598
In summary: The equations of kinematics are a set of equations that govern the motion of an object. They are usually written as:##\mathbf{F}(\mathbf{x},t,\mathbf{t},a)##where:##\mathbf{x}## is the position of the object at time t##\mathbf{t}## is the time##\mathbf{a}## is the acceleration vector.
Runner1598

## Homework Statement

A hot-air balloon is rising upward with a constant speed of 2.20 m/s. When the balloon is 3.30 m above the ground, the balloonist accidentally drops a compass over the side of the balloon. How much time elapses before the compass hits the ground?

## The Attempt at a Solution

I just started taking Physics 1111 at college and never having taken physics in high school, I have no idea where to start. I assume you would use the knowledge that an object falls towards Earth at 9.8 m/s^2... I just don't even know what equation of kinematics to plug this information into? Thank you for your help!

Runner1598 said:

## Homework Statement

A hot-air balloon is rising upward with a constant speed of 2.20 m/s. When the balloon is 3.30 m above the ground, the balloonist accidentally drops a compass over the side of the balloon. How much time elapses before the compass hits the ground?

## The Attempt at a Solution

I just started taking Physics 1111 at college and never having taken physics in high school, I have no idea where to start. I assume you would use the knowledge that an object falls towards Earth at 9.8 m/s^2... I just don't even know what equation of kinematics to plug this information into? Thank you for your help!
You can start by writing the eqs. of kinematics in section 2 of the template. There are only a handful.

You want an equation which relates distance, time, and acceleration.

Starting out, you will do yourself a favor by breaking the problem into parts that are easier to visualize and solve. In this case, what is a good first part of the path of the compass?

What is the initial position?
What is the initial velocity?
What is the constant acceleration?

Remember that velocity can be described by:
##\int_{t_0}^t a(s) ds +v(t_0)= v(t)##
and position can be described by:
##\int_{t_0}^t v(r) dr +p(t_0)= p(t)##.

Is simple integration part of your toolkit? What are the equations of kinematics?

## 1. What is the equation for calculating velocity in kinematics?

The equation for calculating velocity in kinematics is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

## 2. How do you calculate acceleration in kinematics?

Acceleration in kinematics can be calculated using the equation a = (v - u) / t, where a is the acceleration, v is the final velocity, u is the initial velocity, and t is the time.

## 3. Is gravity a factor in kinematics equations?

Yes, gravity is a factor in kinematics equations. It is often represented as the acceleration due to gravity, g, which has a value of approximately 9.8 m/s^2.

## 4. How is displacement calculated in kinematics?

Displacement in kinematics can be calculated using the equation s = ut + 1/2at^2, where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time.

## 5. What is the difference between average velocity and instantaneous velocity in kinematics?

Average velocity is the total displacement divided by the total time taken, while instantaneous velocity is the velocity at a specific moment in time. It can be calculated by taking the derivative of the displacement equation with respect to time.

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