Calculus Word Problems

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Calculus word problems are used to solve the word problems. This tool converts the word problem into

equations and then with the help of the relevant calculus formula, it solves the final equation. This tool is so

efficient that the conversion and solving process goes almost simultaneously, means the time consume is

very less in getting the result.

This can be better clarified by taking individual examples of differentiation and integration. The examples are

as shown below:-



Example 1:- Find the velocity in cm/s if the small displacement is given by 5 cm in time duration of

10 s.



Solution 1:- Given small displacement = 5 cm.

 Let us assume that the small displacement is denoted by dx

 Therefore from above, dx = 5 cm

Also, it is given that this displacement is covered in time duration of 10 s.

This time duration is also very small just 10 s. So we can consider this time as a very small time period, so we

can denote it by dt.

Therefore from above, dt = 10 s.

Now we know that the velocity is the ratio of displacement travelled to the total time taken. And let ‘v’ is the

velocity of an object
                                    V = dx / dt = 5/10 = ½ = 0.5 cm.

Hence , the velocity of an object is 0.5cm


Example 2:- Find the velocity in cm/s if the small displacement is given by 20 m in time duration of

5 s.



Solution 2:-  Given small displacement = 20 cm.

Let us assume that the small displacement is denoted by dx

Therefore from above,dx = 20 cm

Also, it is given that this displacement is covered in time duration of5 s.

This time duration is also very small just 10 s. So we can consider this time as a very small time period, so we

can denote it by dt.

Therefore from above, dt = 5 s.

Now we know that the velocity is the ratio of displacement travelled to the total time taken. And let ‘v’ is the

velocity of an object’
                                    V = dx/dt = 20/5 = 4 = 4 cm/s

Hence the velocity of an object is 4cm/ s. 

 

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