Two cars 'A' and 'B' move on a straight road for the same time. Car 'A' covers \(80 \mathrm{~m}\) and car 'B' covers 100 \(\mathrm{m}\). Which one of the two is faster?

When attempting to understand motion, one of the fundamental concepts we encounter is speed calculation. Speed represents how fast an object is moving and is usually described as a distance covered per unit of time. The formula for calculating speed is quite simple yet fundamentally important: \[ \text{speed} = \frac{\text{distance}}{\text{time}} \].

Let's use this formula to decipher a typical physics problem: comparing the speeds of two cars. If Car A covers 80 meters in a given time (let's say 't' seconds), and Car B covers 100 meters in the same time, we would calculate their speeds as follows:

- Speed of Car A: \( \text{Speed}_A = \frac{80\text{ m}}{t} \)
- Speed of Car B: \( \text{Speed}_B = \frac{100\text{ m}}{t} \).

The key to comparing the speed of both cars effectively is to consider that they travel for the same duration. Thus, to determine which car is faster, we simply compare the distances covered, as their travel times are equal. As 100 meters is more than 80 meters, Car B is, without a doubt, the faster vehicle.

Delving into the distance-time relationship is essential for understanding motion in physics. This relationship tells us how the distance covered by an object correlates with the time it takes to travel that distance. When an object moves at a constant speed, the distance it covers is directly proportional to the travel time. If the speed varies, this relationship can become more complex.

In our example, since the cars move over the same time period, we can make a direct comparison of the distances. We know that Car B has covered a greater distance in the same amount of time, which means it has a higher speed. The distance-time graph for each car would show a straight line (for constant speed), with Car B's line rising more steeply, indicating its greater speed. Understanding this relationship is crucial for solving problems in physics and in everyday scenarios that involve motion.

Motion in physics typically involves an object's displacement over time, and it's described quantitatively by variables such as speed, velocity, and acceleration. Speed is scalar and only denotes how fast something is moving, whereas velocity is a vector, indicating both the speed and direction of movement. Acceleration describes how the velocity changes over time.

In our cars' scenario, we focused solely on speed and distance. However, in more complex situations, we might also consider the direction for velocity or changes in speed for acceleration. For instance, Car A could be increasing its speed (accelerating) as it moves, while Car B could be slowing down (decelerating), but still cover more distance within the same time. Therefore, a full analysis of motion would involve all these factors to get a clear picture of the dynamics involved. By understanding these elements, students can tackle a wider array of problems in physics, ranging from simple speed calculations to complex motion analyses in various dimensions.