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?

Explanation:

Step1: Convert kilometers to meters

We know that \(1\) kilometer \( = 1000\) meters. So, \(100\) km \(=100\times1000\) m \( = 100000\) m.

Step2: Convert hours to seconds

We know that \(1\) hour \(=3600\) seconds.

Step3: Calculate meters per second

The speed \(v\) in meters per second is given by the formula \(v=\frac{\text{distance in meters}}{\text{time in seconds}}\). Substituting the values, \(v=\frac{100000}{3600}\approx27.8\) m/s.

Step4: Convert kilometers per hour to miles per hour

We know that \(1\) kilometer \(=0.621371\) miles. So, if the speed is \(100\) km/h, then in miles per hour, it is \(100\times0.621371\approx62.1\) mph.

Answer:

(a) Approximately \(27.8\) m/s. (b) Approximately \(62.1\) mph.