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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.8, Problem 1E

(a)

To determine

**To find:** The velocity at time *t*.

Expert Solution

The velocity at time is

**Given:**

The given equation is as below.

**Calculation:**

Calculate the velocity at time

Differentiate the equation (1) with respect to time.

Therefore, the velocity at time

(b)

To determine

**To find:** The velocity after 1 second.

Expert Solution

The velocity after 1 second is

Calculate the velocity after 1 second.

Substitute 1 for

Therefore, the velocity after 1 second is

(c)

To determine

**To find:** The time when particle at rest.

Expert Solution

The particle never is at rest.

Calculate the time when particle will be at rest.

The velocity will be zero, when the particle is at rest.

Substitute 0 for

From the above equation, the value of time *t* doesn’t exist. Therefore, the particle never is at rest.

(d)

To determine

**To find:** The particle moving in the positive direction.

Expert Solution

The velocity of particle always moves in positive direction.

Calculate the time at which the particle will be moving in the positive direction.

If speed is positive, the particle moves in positive direction whereas the speed is negative, the particle moves in negative direction.

Substitute 0 for

Therefore, the velocity at

(e)

To determine

**To find:** The total distance traveled during the first 6 seconds.

Expert Solution

The total distance travelled during first 6 seconds is

Calculate the total distance traveled during first 6 seconds.

Substitute 0 for

Substitute 6 for

Therefore, the total distance travelled during first 6 seconds is

(f)

To determine

**To find:** The diagram to illustrate the motion of the particle.

Expert Solution

The diagram is shown in the figure (1).

Show the diagram to illustrate the motion of the particle as shown below in figure (1).

(g)

To determine

**To find:** The acceleration at time *t* and after 1 second.

Expert Solution

The acceleration at time is

Calculate the acceleration at time *t.*

Differentiate the equation (2) with respect to *t.*

Therefore, the acceleration at time is

Calculate the acceleration after 1 second.

Substitute 1 for

Therefore, the acceleration after 1 second is

(h)

To determine

**To sketch:** The graph the position, velocity, and acceleration function for

Expert Solution

Calculate the position using the formula.

Substitute 0 for

Similarly, calculate the remaining values.

Calculate the value of

0 | 0 |

0.5 | 10.125 |

1 | 17 |

1.5 | 21.375 |

2 | 24 |

2.5 | 25.625 |

3 | 27 |

3.5 | 28.875 |

4 | 32 |

4.5 | 37.125 |

5 | 45 |

5.5 | 56.375 |

6 | 72 |

Calculate the velocity using the expression.

Substitute 0 for

Similarly, calculate the remaining values.

Calculate the value of

0 | 24 |

0.5 | 16.75 |

1 | 11 |

1.5 | 6.75 |

2 | 4 |

2.5 | 2.75 |

3 | 3 |

3.5 | 4.75 |

4 | 8 |

4.5 | 12.75 |

5 | 19 |

5.5 | 26.75 |

6 | 36 |

Calculate the acceleration using the formula.

Substitute 0 for

Similarly, calculate the remaining values.

Calculate the value of

0 | -16 |

0.5 | Z-13 |

1 | -10 |

1.5 | -7 |

2 | -4 |

2.5 | -1 |

3 | 2 |

3.5 | 5 |

4 | 8 |

4.5 | 11 |

5 | 14 |

5.5 | 17 |

6 | 20 |

Draw the position as a function of time curve as shown in the figure (1).

Draw the speed as a function of time curve as shown in the figure (2).

Draw the acceleration as a function of time curve as shown in the figure (3).

(i)

To determine

**To find:** The time when the particle is speeding up and slowing down.

Expert Solution

The time when the particle is speeding up is when time *t* is greater than

Calculate the time when particle is speeding up and slowing down.

Substitute 0 for

Substitute

Substitute

Therefore, the acceleration is positive when the value of time is