All Calculus 1 Resources
Example Questions
Example Question #21 : Calculus
What is the velocity function when the position function is given by
.
To find the velocity function, we need to find the derivative of the position function.
So lets take the derivative of with respect to .
The derivative of is because of Power Rule:
The derivative of is due to Power Rule
So...
Example Question #22 : Calculus
What is the velocity when the velocity function is at time ?
To find the velocity at we just plug into the veloctiy function
Example Question #23 : Calculus
Find the velocity function when the position function is
.
To find the veloctiy function, we need to take the derivative of the position function
So would turn into
because of the Power Rule as well as the rule that the derivative of a constant is .
Example Question #21 : Calculus
What is the velocity when the position function is
.
To find the velocity function, we need to take the derivative of the position function in relation to
So
changes into
using the Power Rule
.
Example Question #25 : Calculus
What is the velocity when when the velocity function is
?
To find the velocity at time we plug in for
So
becomes
.
Example Question #26 : Calculus
What is the velocity function when the position function is
?
To find the velocity function we need to take the derivative of the position function
So turns into because of power rule.
Example Question #23 : How To Find Velocity
If models the distance of a projectile as a function of time, find the velocity of the projectile at .
We are given a function dealing with distance and asked to find a velocity. recall that velocity is the first derivative of position. Find the first derivative of h(t) and evaluate at t=15.
Example Question #26 : Velocity
Consider the following position function:
Find the velocity of a paper airplane after seconds whose position is modeled by .
Recall that velocity is the first derivative of position.
To find the velocity after 3 seconds, we need p'(3).
Example Question #27 : Velocity
The velocity of a driver is given by the following vector:
What velocity will she or he reach in the long run?
To find the velocity for the long run, we need to find the limit as t gets bigger and bigger.
Note that to find this limit, we need to take the limit componentwise.
We know the following:
.
Therefore as t becomes bigger we will reach the velocity given by:
Example Question #21 : How To Find Velocity
Two drivers have the following position vectors:
Wich driver is driving faster?
They follow the same path and have the same velocity.
The second driver.
We can't tell from the given information.
The first driver.
They have the same velocity.
The second driver.
To find who is driving faster, we need to compare the norm of their velocities:
We will call the velocities of the first and the second drivers respectively.
Using the Chain Rule on the position function we have the following velocities,
.
.
Now we find the speed of both drivers.
Use the trigonometric identity to find velocity two.
and we see that the second driver is driving faster.