Question

The world record for the women’s $100metre$ sprint in 1993 stood at $10.49seconds.$
a) What average speed does this represent?
b) If the athlete accelerates to a steady speed in the first $1.5seconds$ of the race and then runs at this speed until reaching the finishing line, at what steady speed does she run? (Hint: solve by drawing the velocity-time graph)

Answer 1

a)

Step 1: Given data
$dis\tan ce,d=100metre$
$time,t=10.49seconds.$

Step 2: calculating average speed
$Averagespeed,s=\frac{totaldis\tan ce}{totaltime}=\frac{100}{10.49}=9.53m/s.$.

Hence, her average speed is $9.53m/s$.

b)

Step 1: Given data

Let $x$ represent the steady speed.

Step 2: Area under speed-time graph gives the distance.

The distance is calculated as follows.

$d=\frac{1}{2}\times 1.5\times x+(10.49-1.5)\times x=9.74\times x$

$$\begin{gathered} 9.74\times x=100 \\ x=\frac{100}{9.74} \\ x=10.27m/s \end{gathered}$$

Hence, steady speed with which she runs is $10.27m/s.$