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Make a qualitative graph of speed v versus time t for a falling object (a) for which air resistance can be ignored and (b) for which air resistance cannot be ignored.

6 years ago

We neglect the effect of air resistance and consider the downward motion of the object, and assume that the initial speed of the object to be v

We take the convention that the vectors pointing downwards are taken to be positive.

From the equation of kinematics, we have

v

It is important to realize that the initial velocity and the acceleration due to gravity points in the same direction, therefore the final velocity or the speed increases over time, therefore the final speed can be represented as:

vy = v0y + gt …… (1)

The equation above resembles the equation of straight line of form y = ax + b , where a and b are constants.

Comparing the equation (1) with the standard equation of straight line, we have that the time is represented on x xis while the final speed on y axis such that the constant a and b are g and v

The plot of above equation is shown below:

(b) Now we do not neglect the effect of air resistance and consider the downward motion of the object, and assume that the initial speed of the object to be v

We also assume that the net acceleration of the object is given by , the mass by m and the force of friction by F

From the equation of kinematics, we have

v

It is important to note that here we cannot consider the acceleration of the object to be because of the resistance it experiences from air.

The magnitude of the acceleration can be calculated as:

One can clearly note that if the magnitude of F

If we assume that the magnitude of F

On substituting the value of in the equation of kinematics, we have

Therefore we get a straight line similar to that in above part but the change of speed will be smaller in magnitude relatively as can be seen in the graph below.

The graph between the speed and time in such situation is given below:

It is important to note that in nature, the magnitude of F

The speed-time graph in such a case would resemble like the one shown below:

6 years ago

We neglect the effect of air resistance and consider the downward motion of the object, and assume that the initial speed of the object to be v

We take the convention that the vectors pointing downwards are taken to be positive.

From the equation of kinematics, we have

v

It is important to realize that the initial velocity and the acceleration due to gravity points in the same direction, therefore the final velocity or the speed increases over time, therefore the final speed can be represented as:

vy = v0y + gt …… (1)

The equation above resembles the equation of straight line of form y = ax + b , where a and b are constants.

Comparing the equation (1) with the standard equation of straight line, we have that the time is represented on x xis while the final speed on y axis such that the constant a and b are g and v

The plot of above equation is shown below:

(b) Now we do not neglect the effect of air resistance and consider the downward motion of the object, and assume that the initial speed of the object to be v

We also assume that the net acceleration of the object is given by , the mass by m and the force of friction by F

From the equation of kinematics, we have

v

It is important to note that here we cannot consider the acceleration of the object to be because of the resistance it experiences from air.

The magnitude of the acceleration can be calculated as:

One can clearly note that if the magnitude of F

If we assume that the magnitude of F

On substituting the value of in the equation of kinematics, we have

Therefore we get a straight line similar to that in above part but the change of speed will be smaller in magnitude relatively as can be seen in the graph below.

The graph between the speed and time in such situation is given below:

It is important to note that in nature, the magnitude of F

The speed-time graph in such a case would resemble like the one shown below:

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