Understanding the Motorcycle Speed, Distance, and Time Problem

This question asks us to find the time taken by a motorcycle to cover a specific distance while travelling at a given speed. We are provided with the distance in meters and the speed in kilometers per hour, and we need to find the time in seconds.

Given Information:

• Distance covered by the motorcycle (d) = 1000 m
• Speed of the motorcycle (v) = 36 km/hr

Goal:

Find the time taken (t) in seconds.

Step-by-Step Solution

1. Ensure Consistent Units

Before using any formula relating distance, speed, and time, it is crucial to have all quantities in consistent units. The distance is in meters (m), and we need the time in seconds (s). The speed is given in kilometers per hour (km/hr). We need to convert the speed from km/hr to meters per second (m/s).

To convert km/hr to m/s, we use the conversion factors:

• 1 km = 1000 m
• 1 hour = 60 minutes
• 1 minute = 60 seconds
• So, 1 hour = \(60 \times 60 = 3600\) seconds

Now, let's convert the speed:

Speed (v) in m/s = Speed in km/hr \(\times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ hr}}{3600 \text{ s}}\)

Substituting the given speed:

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

\(v = \frac{36 \times 1000}{3600} \text{ m/s}\)

\(v = \frac{36000}{3600} \text{ m/s}\)

\(v = 10 \text{ m/s}\)

So, the speed of the motorcycle is 10 m/s.

2. Use the Speed, Distance, Time Formula

The fundamental formula relating distance, speed, and time for constant speed is:

Distance = Speed \(\times\) Time

In symbols:

\(d = v \times t\)

We need to find the time (t), so we rearrange the formula:

\(t = \frac{d}{v}\)

3. Calculate the Time

Now we substitute the given distance (d = 1000 m) and the converted speed (v = 10 m/s) into the formula for time:

\(t = \frac{1000 \text{ m}}{10 \text{ m/s}}\)

\(t = 100 \text{ s}\)

The time taken by the motorcycle to cover the distance of 1000 m is 100 seconds.

Conclusion

The time taken by the motorcycle is 100 seconds.

Revision Table: Key Concepts

Additional Information: Understanding Speed, Distance, Time Calculations

Speed, distance, and time problems are common in physics and everyday life. They rely on the basic relationship that speed is the rate at which distance is covered over time. When solving these problems, always pay close attention to the units provided and the units required for the answer.

• Units Consistency: It is essential that the units for distance and time match the units used in the speed measurement. If speed is in m/s, distance should be in meters and time in seconds. If speed is in km/hr, distance should be in kilometers and time in hours. Unit conversion is often the first step.
• The Formula Triangle: A helpful way to remember the relationships \(d = v \times t\), \(v = d/t\), and \(t = d/v\) is the 'distance-speed-time triangle'. Imagine a triangle divided into three sections: Distance at the top, and Speed and Time at the bottom. Covering the variable you want to find shows the formula. For example, covering 'Time' leaves 'Distance over Speed'.
• Constant Speed Assumption: The formulas \(d = v \times t\) work directly only when the speed is constant (uniform motion). If the speed changes, more complex methods (like using average speed or calculus) might be needed. In this problem, we assume constant speed.