Q6P - Fundamentals Of Physics

Question

The 1992 world speed record for a bicycle (human powered vehicle) was set by Chris Huber. His time through the measured 200 m stretch was a sizzling 6.509 sec , at which he commented “Cogito ergo zoom!” (I think, therefore I go fast). In 2001, Sam Whittingham beat Huber’s record by 19.0 km/h. What was Whittingham’s time through the 200 m?

Step-by-Step Solution

Answer

Whittingham’s time through the 200 m was 5.55 sec.

Step 1: Given data

The distance covered,$\Delta x=200 \mathrm{m}$ . 

Time taken by Chris Huber, $\Delta t=6.509 \mathrm{s}$. 

Whittingham’s speed is more by $19.0 \mathrm{km}/\mathrm{h}$. 

Step 2: Understanding the speed

Speed may be defined as the time rate of change in distance. The speed of the cyclist can be found using the given distance and time. 

The expression for the speed is given as follows:

$\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}$

Step 3: Determination of the Whittingham’s speed

Using equation (i), the speed of Huber is calculated as follows:

$\begin{array}{c}\mathrm{Huber}\text{'}\mathrm{s} \mathrm{speed}=\frac{200 \mathrm{m}}{6.509 \mathrm{s}}\\ =30.727 \mathrm{m}/\mathrm{s}\\ =30.727\times \frac{18}{5} \mathrm{km}/\mathrm{h}\\ =110.6 \mathrm{km}/\mathrm{h}\end{array}$

Since Whittingham’s speed is more than Huber by , 

$\begin{array}{c}\mathrm{Whittinghams} \mathrm{speed} =110.6+19.0 \mathrm{km}/\mathrm{h}\\ =129.6 \mathrm{km}/\mathrm{h}\end{array}$

Step 4: Determination of Whittingham’s time

First, convert Whittingham’s speed in m/s.

Distance is given in meters to find time so that we will convert speed into m/s.

$\begin{array}{c}\mathrm{Whittinghams} \mathrm{speed}=129.6 \mathrm{km}/\mathrm{h}\\ =129.6\times \frac{5}{18} \mathrm{m}/\mathrm{s}\\ =36 \mathrm{m}/\mathrm{s}\end{array}$

The time for Whittingham through 200 m was calculated as follows:

$\begin{array}{c}\mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{speed}}\\ =\frac{200 \mathrm{m}}{36 \mathrm{m}/\mathrm{s}}\\ =5.55 \mathrm{s}\end{array}$

Hence, Whittingham’s time through 200 m was 5.55 sec.