Chapter 2, Problem 67A

(a)

To determine

To Plot: The distance travelled by both the cars.

Answer to Problem 67A

Distance travelled by car A is $150\text{km}$ .

Distance travelled by car B is $170\text{km}$ .

Explanation of Solution

Given:

Velocity of car A, $v_A=75\text{km/h}$

Velocity of car B, $v_B=85\text{km/h}$

Time $t=2\text{h}$

Formula used:

Distance can be calculated as:

  $d=v\times t$

Where,

  $v$ is the velocity

  $t$ is the time taken

Calculation:

Distance travelled can be calculated as:

By car A:

  $\begin{array}{l}{d}_A=v_A\times t\\ d_A=75\times 2\\ d_A=150\text{km}\end{array}$

By car B:

  $\begin{array}{l}{d}_B=v_B\times t\\ d_B=85\times 2\\ d_B=170\text{km}\end{array}$

Table shows position with time for both the car is given below:

Time (hour)	Position of car A (km) $d_A=v_A\times t$	Position of car B (km) $d_B=v_B\times t$
1	75	85
2	150	170
3	225	255
4	300	340

Graph shows position with time for both the car is given below:

  

Conclusion:

Distance travelled by car A and car B is $150\text{km}$ and $170\text{km}$ respectively.

(b)

To determine

To Calculate: The time when each car passed the gas station and show them on graph.

Answer to Problem 67A

Car A passed the gas station in $1.4\text{h}$ .

Car B passed the gas station in $1.6\text{h}$ .

Explanation of Solution

Given:

Velocity of car A, $v_A=75\text{km/h}$

Velocity of car B, $v_B=85\text{km/h}$

Distance to the gas station, $d=120\text{km}$

Formula used:

Time can be calculated as:

  $t=\frac{d}{v}$

Where,

  $d$ is the distance

  $v$ is the velocity

Calculation:

Time taken by car A:

  $\begin{array}{l}{t}_A=\frac{d}{v_A}\\ t_A=\frac{120}{75}\\ t_A=1.6\text{h}\end{array}$

Time taken by car A:

  $\begin{array}{l}{t}_B=\frac{d}{v_B}\\ t_B=\frac{120}{85}\\ t_B=1.4\text{h}\end{array}$

Time can also be calculated by graph:

Draw the perpendicular lines from the y-axis to the obtained lines and from these points draw the perpendicular line on x − axis. Obtained intersecting point on the x-axis is the time taken by the cars.

  

Conclusion:

Car A and car B pass the gas station in $1.4\text{h}$ and $1.6\text{h}$ respectively