Chapter 4, Problem 25A

In the speed versus time graphs, all times t are in s and all speeds v are in m/s.

a. From greatest to least, rank the graphs in terms of the greatest speed at 10 seconds.

b. From greatest to least, rank the graphs in terms of the greatest acceleration.

c. From greatest to least, rank the graphs in terms of the greatest distance covered in 10 seconds.

To determine

To rank: The graphs in terms of speed at given time from greatest to least.

Answer to Problem 25A

Rank of graph in terms of greatest speed at 10 seconds is $A=C,B$ .

Explanation of Solution

Given:

The given graphs are shown below:

  

Given time is 10 seconds.

Calculation:

In graph A,

At 10 seconds, values of speed $v=30\frac{m}{s}$

In graph B,

At 10 seconds, values of speed $v=3\frac{m}{s}$

In graph C,

At 10 seconds, values of speed $v=10\frac{m}{s}$

Conclusion:

Therefore, rank of graph in terms of greatest speed at 10 seconds is $A=C,B$

To determine

To rank: The given graphs in terms of greatest acceleration from greatest to least.

Answer to Problem 25A

Ranking of graphs in terms of greatest acceleration is $C,A=B$ .

Explanation of Solution

Given:

The given graphs are shown below:

  

Formula used:

In speed versus time graphs, acceleration is defined as,

  $a=\frac{\Delta v}{\Delta t}$

Where,

  $\Delta v$ = change in speed

  $\Delta t$ = Time interval

Calculation:

From graph-A,

  $\Delta v=0$

Hence,

  $a=0$

From graph-B,

  $\Delta v=0$

Hence,

  $a=0$

From graph-C,

  $\Delta v=10\frac{\text{m}}{\text{s}}$

  $\Delta t=10\text{s}$

Hence,

  $a=1\frac{m}{s^2}$

Conclusion:

Ranking of graphs in terms of greatest acceleration is $C,A=B$

To determine

To rank: The graphs in terms of greatest distance covered in given time from greatest to least.

Answer to Problem 25A

Ranking of graphs in terms of greatest distance covered is A, C, B.

Explanation of Solution

Given:

The given graphs are shown below:

  

Given time is 10 seconds.

Formula used:

The distance covered by an object from the velocity-time graph is equal to the area under the curve.

  $d=$ Area under the curve

Calculation:

From graph-A,

Area covered by the graph is rectangular shape.

Hence,

  $d=30\times 10$

  $d=300$ m

From graph-B,

Area covered by the graph is rectangular shape.

Hence,

  $d=3\times 10$

  $d=30$ m

From graph-C,

Area covered by the graph is triangular shape.

Hence,

  $d=\frac{1}{2}\times 10\times 10$

  $d=50$ m

Conclusion:

Ranking of graphs in terms of greatest distance covered is A, C, B.