Calculus 2 : Applications in Physics

Example Questions

Example Question #3 : Initial Conditions

Find the work done by gravity exerting an acceleration of   for a   block down  from its original position with no initial velocity.

Remember that

, where  is a force measured in  is work measured in , and  and  are initial and final positions respectively.

Explanation:

The force of gravity is proportional to the mass of the object and acceleration of the object.

Since the block fell down 5 meters, its final position is  and initial position is .

Example Question #181 : Integrals

The velocity of a car is defined by the equation , where  is the time in minutes. What distance (in meters) does the car travel between  and ?

Explanation:

We define velocity as the derivative of distance, or .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or

Since , we can use the Power Rule for Integrals

for all ,

to find:

Example Question #182 : Integrals

The velocity of a train is defined by the equation , where  is the time in seconds What distance (in meters) does the train travel between  and ?

Explanation:

We define velocity as the derivative of distance, or .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or

Since , we can use the Power Rule for Integrals

for all ,

to find:

Example Question #183 : Integrals

The velocity of a balloon is defined by the equation , where  is the time in minutes. What distance (in meters) does the balloon travel between  and ?

Explanation:

We define velocity as the derivative of distance, or .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or

Since , we can use the Power Rule for Integrals

for all ,

to find:

Example Question #184 : Integrals

A frisbee has a velocity defined by , where we express  in seconds. What distance does it travel between  in meters?

Explanation:

We define velocity as the derivative of distance, or .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or

.

Since

,

we can use the Power Rule for Integrals

for all ,

to find:

Example Question #191 : Integrals

A ball has a velocity defined by , where we express  in seconds. What distance does it travel between  in meters?

None of the above

Explanation:

We define velocity as the derivative of distance, or .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or .

Since

, we can use the Power Rule for Integrals

for all ,

to find:

Example Question #11 : Applications In Physics

A subway has a velocity defined by , where we express  in seconds. What distance does it travel between  in meters?

Explanation:

We define velocity as the derivative of distance, or .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or .

Since

,

we can use the Power Rule for Integrals

for all ,

to find:

Example Question #193 : Integrals

A train goes a certain distance between  (where  is time in seconds). If we know that the train's velocity is defined as , what is the distance it travelled (in meters)?

Explanation:

We define velocity as the derivative of distance, or .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or .

Since , we can use the Power Rule for Integrals

for all ,

to find:

Example Question #194 : Integrals

A car goes a certain distance between  (where  is time in seconds). If we know that the car's velocity is defined as , what is the distance it travelled (in meters)?

Explanation:

We define velocity as the derivative of distance, or .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or .

Since , we can use the Power Rule for Integrals

for all ,

to find:

Example Question #195 : Integrals

A plane goes a certain distance between  (where  is time in seconds). If we know that the plane's velocity is defined as , what is the distance it travelled (in meters)?

Explanation:

We define velocity as the derivative of distance, or .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or .

Since , we can use the Power Rule for Integrals

for all ,

to find: