Chapter 2, Problem 31P

To determine

The time required to accelerate in order to achieve the desired time.

Answer to Problem 31P

3.1 seconds.

Explanation of Solution

Given:

Race track is 10,000 m that a runner is expected to cover in less than 30 min.

But after 27 mins,a runner still have to cover 1100 m.

Formula used:

The kinematics equation is

  $v=u+at$

Here,

v is final velocity

t is time

a is acceleration

u is initial velocity

Calculation:

Distance covered in 27 minutes is,

  $\begin{array}{c}d=10,000-1100\\ =8,900\text{m}\end{array}$

So, speed of the runner for 27 min is,

  $\begin{array}{c}v=\frac{d}{t}\\ =\frac{8,900}{27\times 60}\\ =5.49\sec \end{array}$

Now the runner has remaining 3 minute to cover the distance. let he will accelerate for t seconds

For 3 min, the speed will be,

  $\begin{array}{c}{v}_1=\frac{1100}{3\times 60}\\ =6.11\text{m}/\text{s}\end{array}$

Using the kinematics equation,

  $\begin{array}{l}v=u+at\\ 6.11=5.49+\left(0.2\right)t\\ t=\frac{6.11-5.49}{0.2}=3.1\text{sec}\end{array}$

Conclusion:

Therefore, time in seconds is 3.1 seconds.