Chapter 0.1, Problem 13E

To determine

The position of the bicycle rider at the given time $t$ .

Answer to Problem 13E

The position of the bicycle rider at the time $t=8$ minutes is $5.8\text{km}$ .

Explanation of Solution

Given:

At Time $t=6$ minutes,

Position $d=5\text{km}$

Bicycle rider travels $2\text{km}$ in every $5\min$

At $t=8\min ?$

Calculation:

Find the position of the bicycle rider at the time $t=8$

minutes:

Assume that, the vehicle moves in positive direction.

A position at $t=6$ is given, and a position at $t=8$ is asked:

So, the difference between these two points are:

  $8\min -6\min =2\min$

So, if the bicycle rider travels $2\text{km}$ in every $5\min$ , then the distance travelled in $1\min$ is:

  $\frac{2\text{km}}{5\min }=0.4\text{km}$

Thus, the bicycle rider travels $0.4\text{km}$ in $1\min$ .

Find the bicycle rider travels in $2\min$ :

  $0.4\text{km}\times 2\min =0.8\text{km}$

To find the new position of the bicycle rider, add $0.8\text{km}$ with the initial stage position $d=5\text{km}$ :

  $\begin{array}{l}d=5\text{km}+0.8\text{km}\\ d=5.8\text{km}\end{array}$

Hence, the position of the bicycle rider at the time $t=8$ minutes is $5.8\text{km}$ .