Calculus 1 : Calculus
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Example Question #151 : Calculus
If 
If p(t) models the position of an electron as a function of time. Find the velocity of the electron when
If p(t) models the position of an electron as a function of time. Find v(t), the velocity function of the electron:
Recall that velocity is the derivative of position. To find v(t), we need to find p'(t)
Remember that the derivative of cosine is negative sine, so we get...
We are almost there, but we need to find the velocity at the given time, not just the velocity function.
So our answer is:
Example Question #151 : Spatial Calculus
The acceleration due to gravity, in meters per second squared, on Earth is described by the function
Which function describes the velocity of a ball thrown at an initial velocity of 15 meters per second?
The velocity function is found by taking the antiderivative of acceleration.
The initial velocity is the velocity when t = 0. We can use v(0) = 15 to find the constant c.
Therefore, the function describing velocity is
Example Question #153 : Calculus
The initial velocity of a particle is 
Velocity can be found as the integral of acceleration with respect to time:
To find the constant of integration, utilize the initial condition, i.e. the initial velocity:
Thus
And
Example Question #154 : Calculus
The location of a particle is given by the function 
What is its velocity at 
Velocity is given by the derivative of the position function with respect to time:
Utilizing the product rule of derivatves, which follows the form:
We find velocity to be:
Example Question #155 : Calculus
The acceleration of a particle is given by the function 
Velocity can be found by integrating acceleration with respect to time:
To find the integration of constant, utilize the initial velocity:
Now, to find the average velocity, integrate the velocity function once more over the interval and divide by the interval:
Example Question #156 : Calculus
What is the velocity of a particle at 
Velocity can be found as the time derivative of position:
Therefore, at 
Example Question #157 : Calculus
Let
be the position function of a particle moving on a coordinate line, where 
The instantaneous velocity is simply the derivative of the position function with respect to time:
Therefore:
To find the instantaneous velocity at t=3 seconds:
Example Question #158 : Calculus
If the position of a particle is defined by the function:
What is the velocity of the particle at 
Recall that the velocity of moving body can be computed from its position function by taking the first derivative of that function. Thus, we know that:
This is relatively easy for our data:
Thus, the velocity of the particle is
Example Question #159 : Calculus
The position of a particle is defined by the following function:
What is the velocity of the particle at time 
To find the velocity of a moving body based on its position function, you need to take the first derivative of that position function. Thus, we know, using the product rule that:
To calculate the velocity, you merely need to find the value of 
Example Question #160 : Calculus
The acceleration of a particle vibrating back and forth across an vertical post is defined by the equation:
What is the velocity of the particle at time 
Recall that the velocity of a body can be calculated by taking the integral of its acceleration function, thus, we know:
This would be:
Thus, we can find the velocity of this body by solving for 
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