Chapter 2, Problem 68A

To determine

To Draw: The position time graph for each car and find when does each car get to the beach.

Explanation of Solution

Given:

Distance, $d=50\text{km}$

Velocity of car A, $v_A=40\text{km/h = 0}\text{.67}\text{km/min}$

Initial displacement of car A, $d_i=10\text{km}$

Velocity of car B, $v_B=100\text{km/h = 1}\text{.67}\text{km/min}$

Initial displacement of car B, $d_i=0$

Formula used:

Distance can be calculated as:

  $d=vt+d_i$

Where,

  $v$ is the velocity

  $t$ is the time taken

  $d_i$ initial position

Calculation:

Table for displacement for each car with time is shown below:

Time for car A	Displacement for car A   $d=vt+d_i$	Time for car B	Displacement for car B   $d=vt+d_i$
0 min 12 noon	10 km	0 min 12:30 noon	0
10 min 12:10 noon	16.7 km	10 min 12:40 noon	16.7
20 min 12:20 noon	23.4 km	20 min 12:50 noon	33.4
30 min 12:30 noon	30.1 km	30 min 1:00 pm	50.1
40 min 12:40 noon	36.8 km	40 min 1:10 pm	66.8
50 min 12:50 noon	43.5 km	50 min 1:20 pm	83.5
60 min 1:00 pm	50.2 km	60 min 1:30 pm	100.2

Graph can be drawn as:

  

From the graph it is clear that both car will arrived at $1\text{p}\text{.m}\text{.}$

Conclusion:

Each car gets to the beach at $1\text{p}\text{.m}\text{.}$