Calculating Average Speed of a Car

The problem asks us to find the average speed of a car in kilometers per hour (km/hr), given the distance it covers and the time taken. We are given the distance in meters (m) and the time in seconds (s).

Understanding Average Speed

Average speed is defined as the total distance covered divided by the total time taken. The formula is:

\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)

In this question, the given values are:

• Total Distance = 400 m
• Total Time = 20 seconds

Step-by-Step Calculation in m/s

First, let's calculate the average speed in meters per second (m/s) using the formula:

\(\text{Average Speed} = \frac{400 \text{ m}}{20 \text{ s}}\)

\(\text{Average Speed} = 20 \text{ m/s}\)

So, the average speed of the car is 20 m/s.

Converting Speed from m/s to km/hr

The question requires the answer in kilometers per hour (km/hr). We need to convert the speed from m/s to km/hr. The conversion factor is:

• 1 kilometer (km) = 1000 meters (m)
• 1 hour (hr) = 60 minutes = 60 \(\times\) 60 seconds = 3600 seconds (s)

Therefore, to convert m/s to km/hr, we can multiply the speed in m/s by \(\frac{\text{Distance conversion factor}}{\text{Time conversion factor}}\). Let's derive the conversion:

\(1 \text{ m/s} = \frac{1 \text{ m}}{1 \text{ s}}\)

To convert meters to kilometers, we divide by 1000 (or multiply by \(\frac{1}{1000}\) km/m).

To convert seconds to hours, we divide by 3600 (or multiply by \(\frac{1}{3600}\) hr/s).

\(1 \text{ m/s} = \frac{1 \text{ m}}{1 \text{ s}} = \frac{\frac{1}{1000} \text{ km}}{\frac{1}{3600} \text{ hr}} = \frac{1}{1000} \times 3600 \text{ km/hr} = \frac{3600}{1000} \text{ km/hr} = \frac{36}{10} \text{ km/hr} = \frac{18}{5} \text{ km/hr}\)

So, to convert speed from m/s to km/hr, we multiply by \(\frac{18}{5}\).

Final Speed Calculation in km/hr

Now, we convert the calculated speed of 20 m/s to km/hr:

\(\text{Average Speed (km/hr)} = \text{Average Speed (m/s)} \times \frac{18}{5}\)

\(\text{Average Speed (km/hr)} = 20 \times \frac{18}{5}\)

We can simplify the calculation:

\(\text{Average Speed (km/hr)} = (20 \div 5) \times 18\)

\(\text{Average Speed (km/hr)} = 4 \times 18\)

\(\text{Average Speed (km/hr)} = 72 \text{ km/hr}\)

Thus, the average speed of the car is 72 km/hr.

Revision Table: Important Formulas

Additional Information: Speed, Velocity, and Units

Understanding speed and its units is fundamental in physics. Here are some related concepts:

• Speed vs. Velocity: Speed is a scalar quantity that measures how fast an object is moving. Velocity is a vector quantity that includes both speed and direction. Average speed is the total distance over total time, while average velocity is the total displacement over total time.
• Instantaneous Speed: This is the speed of an object at a particular moment in time, as opposed to average speed which is over a duration.
• Common Units: The standard SI unit for speed is meters per second (m/s). Other common units include kilometers per hour (km/hr), miles per hour (mph), and feet per second (ft/s). Being able to convert between these units is a key skill.
• Distance and Displacement: Distance is the total path length covered by an object. Displacement is the straight-line distance between the starting and ending points, including direction. For calculating average speed, we use the total distance.