# How do I find the speed of an object with a given position function?

• Math10
In summary, the speed of an object with r(t)=e^(t)<cos(t), sin(t), 1> can be found by taking the absolute value of the vector v(t)=e^(t)<cos(t)-sin(t), cos(t)+sin(t), 1>. The answer in the book is sqrt(3)*e^(t).
Math10

## Homework Statement

Find the speed of an object with r(t)=e^(t)<cos(t), sin(t), 1>.

None.[/B]

## The Attempt at a Solution

v(t)=e^(t)<cos(t)-sin(t), cos(t)+sin(t), 1>
I know that the speed is abs(v(t)) and the answer in the book is sqrt(3)*e^(t). So how do I find the speed?

Math10 said:

## Homework Statement

Find the speed of an object with r(t)=e^(t)<cos(t), sin(t), 1>.

None.[/B]

## The Attempt at a Solution

v(t)=e^(t)<cos(t)-sin(t), cos(t)+sin(t), 1>
I know that the speed is abs(v(t)) and the answer in the book is sqrt(3)*e^(t). So how do I find the speed?
The speed is the magnitude of your vector for v(t). How do you usually find the magnitude of a vector?

Never mind, I got it! Thanks for helping.

## 1. How do you calculate the speed of an object?

The speed of an object can be calculated by dividing the distance it travels by the time it takes to travel that distance. The formula for speed is speed = distance/time.

## 2. What units are used to measure speed?

The most common units used to measure speed are meters per second (m/s) and kilometers per hour (km/h). However, other units such as miles per hour (mph) and feet per second (ft/s) can also be used.

## 3. What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of both speed and direction. In other words, velocity takes into account the direction in which the object is moving, while speed does not.

## 4. Can the speed of an object change?

Yes, the speed of an object can change if it accelerates or decelerates. Acceleration is the rate at which an object's speed changes over time. An object can also change direction without changing its speed, in which case its velocity would change but not its speed.

## 5. How is speed related to other physical quantities?

Speed is related to distance and time, as it is calculated by dividing distance by time. It is also related to acceleration, as an object's speed can change due to acceleration. Additionally, speed is a scalar quantity, meaning it only has magnitude, while velocity is a vector quantity, meaning it has both magnitude and direction.

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