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Aneli [31]
2 years ago
15

If a particle moving in a circular path of radius 5 m has a velocity function v = 4t2 m/s, what is the magnitude of its total ac

celeration at t = 1 s?
Engineering
2 answers:
rjkz [21]2 years ago
5 0

Answer:

8.62m/s²

Explanation:

the particle is experiencing both translational and circular motion

v=4t²

a_{t}=\frac{dv}{dt}=8t

at t=1s, \frac{dv}{dt}=8(1)=8m/s²

a_{c} = \frac{v^{2} }{r}

at t=1, v= 4(1)² = 4m/s

a_{c}=4²/5

a_{c}=3.2m/s²

∴ magnitude of total acceleration, a

a=\sqrt{a_{t} ^{2} + a_{c} {2} }

a=\sqrt{8^{2} +3.2^{2}  }

a=\sqrt{64+10.24}

a=\sqrt{74.24}

a=8.62m/s²

bija089 [108]2 years ago
5 0
<h2>Answer:</h2>

8.62m/s²

<h2>Explanation:</h2>

The total acceleration (a) of a particle undergoing a circular motion is given by the vector sum of the tangential acceleration (a_{T}) and the centripetal or radial acceleration (a_{C}) of the particle. The magnitude of this total acceleration is given as follows;

a = \sqrt{(a_{T} )^2 + (a_{C} )^2}                  ------------------(i)

(i) But;

a_{T} = time rate of change of velocity (v) = Δv / Δt = \frac{dv}{dt}

<em>From the question,</em>

v = 4t²      -------------------(ii)

Therefore, differentiating equation (ii) with respect to t gives the tangential acceleration as follows;

a_{T} = dv / dt  = \frac{dv}{dt} = \frac{d(4t^{2} )}{dt}

a_{T} = 8t

Now, at time t = 1s, the tangential acceleration is given by substituting t = 1 into equation (iii) as follows;

a_{T} = 8(1)

a_{T} = 8m/s²

(ii) Also;

a_{C} = \frac{v^2}{r}   ------------------------ (iv)

<em>Where;</em>

r = radius of the circular path of motion = 5m

v = velocity of motion = 4t²

<em>Substitute these values into equation (iv) as follows;</em>

a_{C} = \frac{(4t^2)^2}{5}        -------------------------------(v)

Now, at time t = 1s, the centripetal acceleration is given by substituting t = 1 into equation (v) as follows;

a_{C} = \frac{(4(1)^2)^2}{5}

a_{C} = \frac{(4)^2}{5}

a_{C} = \frac{16}{5}

a_{C} = 3.2m/s²

(iii) Now substitute the values of a_{T} and a_{C} into equation (i) as follows;

a = \sqrt{(8)^2 + (3.2)^2}

a = \sqrt{(64) + (10.24)}

a = \sqrt{74.24}

a = 8.62 m/s²

Therefore, the magnitude of the total acceleration at t = 1s is 8.62m/s²

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Answer:

Below is the required code:

Explanation:

Using for loop

#include <iostream>

using namespace std;

int main()

{

    //Initial crud size

    int init = 0;

    int newCrud;

    int next=0;

    //Number of days to simulate

    int no_days;

    int day;

    cout << "Enter initial amount of green crud: ";

    cin >> newCrud;

    cout << "Enter number of days to simulate: ";

    cin >> no_days;

    for (day = 10; day<=no_days; day++)

    {

         if (day % 10 == 0)

         {

             next = newCrud + init;

         }

             newCrud = init;

             init = next;

    }

    if (no_days < 5)

    cout << "\nCrud reproduce only after 5 days minimum.Hence the current amount is "

    << newCrud << " pounds.";

    else

    cout << "On day " << no_days << " you have " << init

    << " pounds of green crud." << endl;

    cout << "\nWould you like to continue? (y or n): ";

    cin >> ans;

         return 0;

}

Output:

         Enter initial amount of green crud: 5

         Enter number of days to simulate: 220

    On day 220 you have 10485760 pounds of green crud.

Using while loop

Program:

#include <iostream>

using namespace std;

int main()

{

    char ans='y';

    while (ans == 'Y' || ans == 'y')

    {

         //Initial crud size

         int init = 0;

         int newCrud;

         int next=0;

         //Number of days to simulate

         int no_days;

         int day;

         cout << "Enter initial amount of green crud:

         ";

         cin >> newCrud;

         cout << "Enter number of days to simulate:

         ";

         cin >> no_days;

         for (day = 10; day<=no_days; day++)

         {

             if (day % 10 == 0)

             {

                  next = newCrud + init;

             }

                  newCrud = init;

                  init = next;

         }

         if (no_days < 5)

         cout << "\nCrud reproduce only after 5 days

         minimum.Hence the current amount is "

         << newCrud << " pounds.";

         else

         cout << "On day " << no_days << " you have "

         << init

         << " pounds of green crud." << endl;

         cout << "\nWould you like to continue? (y or

         n): ";

         cin >> ans;

    }

    return 0;

}

Output:

Enter initial amount of green crud: 5

Enter number of days to simulate: 220

On day 220 you have 10485760 pounds of green crud.

Would you like to continue? (y or n): y

Enter initial amount of green crud: 5

Enter number of days to simulate: 225

On day 225 you have 10485760 pounds of green crud.

Using do while loop

Program:

#include <iostream>

using namespace std;

int main()

{

    char ans;

    do

    {

         //Initial crud size

         int init = 0;

         int newCrud;

         int next=0;

         //Number of days to simulate

         int no_days;

         int day;

         cout << "Enter initial amount of green crud: ";

         cin >> newCrud;

         cout << "Enter number of days to simulate: ";

         cin >> no_days;

         for (day = 10; day<=no_days; day++)

         {

             if (day % 10 == 0)

             {

                  next = newCrud + init;

             }

                  newCrud = init;

                  init = next;

         }

         if (no_days < 5)

         cout << "\nCrud reproduce only after 5 days

         minimum.Hence the current amount is "

         << newCrud << " pounds.";

         else

         

         cout << "On day " << no_days << " you have " <<

         init << " pounds of green crud." << endl;

         cout << "\nWould you like to continue? (y or n):

         ";

         cin >> ans;

    } while (ans == 'Y' || ans == 'y');

    return 0;

}

Output:

Enter initial amount of green crud: 5

Enter number of days to simulate: 220

On day 220 you have 10485760 pounds of green crud.

Would you like to continue? (y or n): y

Enter initial amount of green crud: 5

Enter number of days to simulate: 225

On day 225 you have 10485760 pounds of green crud.

7 0
3 years ago
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