Question

1.2 physical quantities and units

1. the speed limit on some interstate highways is roughly 100 km/h. (a) what is this in meters per second? (b) how many miles per hour is this?
2. a car is traveling at a speed of 33 m/s. (a) what is its speed in kilometers per hour? (b) is it exceeding the 90 km/h speed limit?
3. show that 1.0 m/s = 3.6 km/h. hint: show the explicit steps involved in converting 1.0 m/s = 3.6 km/h.
4. american football is played on a 100 - yd - long field, excluding the end zones. how long is the field in meters? (assume that 1 meter equals 3.281 feet.)

Explanation:

1.

Step1: Convert km to m and h to s

We know that $1\ km = 1000\ m$ and $1\ h=3600\ s$. To convert $100\ km/h$ to $m/s$, we use the conversion factors.
$100\frac{km}{h}\times\frac{1000\ m}{1\ km}\times\frac{1\ h}{3600\ s}=\frac{100\times1000}{3600}\ m/s=\frac{100000}{3600}\ m/s\approx 27.8\ m/s$

Step2: Convert km to miles

We know that $1\ km\approx0.621371$ miles. So, $100\ km/h\times0.621371\frac{miles}{km}=62.1\ miles/h$

Step1: Convert m to km and s to h

We know that $1\ m=\frac{1}{1000}\ km$ and $1\ s=\frac{1}{3600}\ h$. So for a speed of $33\ m/s$, the speed in $km/h$ is $33\frac{m}{s}\times\frac{1\ km}{1000\ m}\times\frac{3600\ s}{1\ h}=\frac{33\times3600}{1000}\ km/h = 118.8\ km/h$

Step2: Compare with speed - limit

Since $118.8\ km/h>90\ km/h$, the car is exceeding the speed - limit.

Step1: Convert m to km and s to h

We start with $1.0\ m/s$. Since $1\ m=\frac{1}{1000}\ km$ and $1\ s=\frac{1}{3600}\ h$, then $1.0\frac{m}{s}=1.0\times\frac{1\ km}{1000\ m}\times\frac{3600\ s}{1\ h}=\frac{3600}{1000}\ km/h = 3.6\ km/h$

Answer:

(a) $27.8\ m/s$
(b) $62.1\ miles/h$

2.