Chapter 2, Problem 53P

(a)

To determine

The average acceleration of the car when it is in first gear

Answer to Problem 53P

The average acceleration of the car when it is in first gear is $3.5{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

The given graph is shown below.

  

Formula used:

Acceleration would be $a=\frac{\Delta v}{\Delta t}=\frac{v_2-v_1}{t_2-t_1}$

Calculation:

Average acceleration in first gear will be $a_1=\frac{(14-0)\text{m/s}}{(4-0)\mathrm{s}}=3.5{\text{m/s}}^{\text{2}}$

Conclusion:

Thus, the average acceleration of the car when it is in first gear is $3.5{\text{m/s}}^{\text{2}}$

(b)

To determine

The average acceleration of the car when it is in third gear.

Answer to Problem 53P

The average acceleration of the car when it is in third gear is $2.6{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

The given graph is shown below.

  

Formula used:

Acceleration would be $a=\frac{\Delta v}{\Delta t}=\frac{v_2-v_1}{t_2-t_1}$

Calculation:

Average acceleration in third gear will be $a_3=\frac{(36-24)\text{m/s}}{(14-9)\text{s}}=2.6{\text{m/s}}^{\text{2}}$

Conclusion:

Thus, the average acceleration of the car when it is in third gear is $2.{\text{6m/s}}^{\text{2}}$

(c)

To determine

The average acceleration of the car when it is in fifth gear.

Answer to Problem 53P

The average acceleration of the car when it is in fifth gear is $0.347{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

Given:

The given graph is shown below.

  

Formula used:

Acceleration would be $a=\frac{\Delta v}{\Delta t}=\frac{v_2-v_1}{t_2-t_1}$

Calculation:

Average acceleration in fifth gear will be $a_5=\frac{(52-44)\text{m/s}}{(50-27)\text{s}}=0.34{\text{7m/s}}^{\text{2}}$

Conclusion:

Thus, the average acceleration of the car when it is in fifth gear is $0.347{\text{m/s}}^{\text{2}}$

(d)

To determine

The average acceleration through the first four gears?

Answer to Problem 53P

The average acceleration through the first four gears is $1.63{\text{m/s}}^{\text{2}}$ .

Explanation of Solution

Given:

The given graph is shown below.

  

Formula used:

Acceleration would be $a=\frac{\Delta v}{\Delta t}=\frac{v_2-v_1}{t_2-t_1}$

Calculation:

Average acceleration through the first four gears will be

  $\begin{array}{c}a=\frac{\Delta v}{\Delta t}\\ =\frac{(44-0)\text{m/s}}{(27-0)\text{s}}\\ =1.6{\text{3m/s}}^{\text{2}}\end{array}$

Conclusion:

Thus, the average acceleration through the first four gears is $1.63{\text{m/s}}^{\text{2}}$