# Velocity as Function of Time

• MPH28
In summary, the conversation discussed finding the velocity of a rock thrown at an angle from an initial height. The equations Vxo=(Vo)(cos[theta]) and Vyo=(Vo)(sin[theta]) were mentioned, along with the need to find the vertical and horizontal components of the velocity. The final equation v(t)=[(Vxo/cos[theta])+(Vyo/sin[theta])]+at was suggested, but it was pointed out that a diagram and trigonometric identities would also be necessary to find the magnitude and angle of the velocity as a function of time.

## Homework Statement

Okay so, a rock is throw from an initial height, ho, at a speed, vo, and an angle [theta] from the horizontal. Find the rocks velocity as a function of time.

## Homework Equations

Vxo=(Vo)(cos[theta])
Vyo=(Vo)(sin[theta])
Acceleration is constant.

## The Attempt at a Solution

Well I know that V(t)=Vo+at

But since the rock is thrown from an angle I got confused. Do I have to replace the Vo with the two equations for the x and y component of velocity? Since I can solve for Vo, but then it is equal to two different things.
Thanks!

Find the vertical component of the velocity and find the horizontal component of the velocity.

With the vertical component you can find out how long it takes for the ball to reach maximum height, where vf = 0

Then find out how high it rises and add the initial height from which it was thrown from and you will be able to get the total flight time.

How do I find out the components if I am not given any numbers?

You are not going to have a number as your answer. It sounds as if you will have an algebraic expression that includes the variable t for time.

You have the right start, certainly find the components in the x- and y- directions. Then treat them like vector and add them together. Note that your "acceleration is constant" statement is incomplete. You have a lot more information than that.

So is my final equation?:

v(t)=[(Vxo/cos[theta])+(Vyo/sin[theta])]+at

No. You'll need to draw a picture with the x- and y- component vectors. To find the magnitude, you'll need the pythagorean theorem. To find the angle (also a function of time), you'll need a trig identity.

## What is velocity as a function of time?

Velocity as a function of time is a mathematical representation of how an object's velocity changes over a period of time. It is typically graphed as a curve, with time on the x-axis and velocity on the y-axis.

## How is velocity as a function of time related to acceleration?

Velocity as a function of time is directly related to acceleration, as acceleration is the rate of change of velocity over time. This means that the slope of a velocity vs. time graph represents the object's acceleration at that moment in time.

## What is the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement of an object divided by the total time taken, while instantaneous velocity is the velocity of an object at a specific moment in time. In other words, average velocity is an average over a period of time, while instantaneous velocity is the velocity at a single point in time.

## How does the shape of a velocity vs. time graph indicate an object's motion?

The shape of a velocity vs. time graph can indicate an object's motion in several ways. A straight line indicates constant velocity, a positive slope indicates constant acceleration, and a horizontal line indicates zero acceleration. Additionally, the area under the curve represents the object's displacement.

## How is velocity as a function of time used in real-world applications?

Velocity as a function of time is used in various real-world applications, such as analyzing the motion of objects in sports, predicting the trajectory of a projectile, and designing transportation systems. It is also used in engineering and physics to understand the behavior of moving objects and to make predictions about their future motion.