# Velocity as a function of time?

• bullroar_86
In summary, to find the velocity of an object with an acceleration of 22.3 m/s^2 [63.9 degrees E of S], you need to find a function v(t) that relates the speed of the object and the time elapsed. This function can be represented by the equation v=vnot+at, where vnot represents the velocity at t=0 and a is the constant acceleration. It is important to note that the velocity is a vector, not just a number.

#### bullroar_86

if an object has an acceleration of 22.3 m/s^2 [63.9 degrees E of S]

what is its "velocity as a function of time"

not sure what that means.. any ideas?

bullroar_86 said:
if an object has an acceleration of 22.3 m/s^2 [63.9 degrees E of S]

what is its "velocity as a function of time"

not sure what that means.. any ideas?

It means you have to find a function v(t) that relates the speed of the object, and the time elapsed.

Hint: The answer is in the definition of (constant) acceleration.

v=vnot+at
vnot equals acceleration from the beginning of the problem.
v= velocity at a given time.

ayalam said:
v=vnot+at
vnot equals acceleration from the beginning of the problem.
v= velocity at a given time.

No, in that equation, "vnot" has to be the velocity at t= 0. And be sure to note that the velocity is a vector, not just a number.

## 1. What is velocity as a function of time?

Velocity as a function of time is the rate of change of an object's displacement over time. It is a mathematical representation of an object's motion, showing how its velocity changes as time passes.

## 2. How is velocity as a function of time calculated?

Velocity as a function of time can be calculated by taking the derivative of an object's position with respect to time. This can be done using the formula v(t) = x'(t), where v(t) is the velocity, x(t) is the position, and ' indicates the derivative.

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

Average velocity is the total displacement of an object divided by the total time it takes to travel that distance. Instantaneous velocity, on the other hand, is the velocity of an object at a specific moment in time.

## 4. How does acceleration affect velocity as a function of time?

Acceleration is the rate of change of velocity over time. It can either increase or decrease an object's velocity depending on its direction. If the acceleration is in the same direction as the velocity, the object will speed up. If the acceleration is in the opposite direction, the object will slow down.

## 5. What are some real-life examples of velocity as a function of time?

There are many examples of velocity as a function of time in everyday life, such as a car accelerating from a stop sign, a cyclist pedaling up a hill, or a ball being thrown into the air. These all involve changes in velocity over time due to acceleration or deceleration.