Question

In a game of billiards you give the ball a speed of \(0.76 \mathrm{~m} / \mathrm{s}\). How much time does it take for the ball to cover a distance of \(0.23 \mathrm{~m}\) ?

Short answer

The ball takes approximately 0.303 seconds.

Step-by-step solution

Identify Given Values

We know the speed of the ball is \(0.76 \, \text{m/s}\) and the distance it needs to cover is \(0.23 \, \text{m}\). These values will be used to find the time.

Use the Formula for Time

The formula to calculate time when speed and distance are known is \( \text{time} = \frac{\text{distance}}{\text{speed}} \). We use this formula to find the time it takes for the ball to cover the specified distance.

Plug in the Values

Substitute the given values into the formula: \( \text{time} = \frac{0.23}{0.76} \).

Calculate the Time

Perform the division: \( \frac{0.23}{0.76} \approx 0.3026 \). Thus, the time taken is approximately \(0.3026 \, \text{s}\).

Conclusion

The ball takes approximately \(0.303 \, \text{s}\) to cover a distance of \(0.23 \, \text{m}\).

Key concepts

Understanding Distance

Distance is a measure of how far an object travels from one point to another. It is typically measured in meters (m) and is a fundamental concept in understanding motion. When calculating problems involving motion, distance is a crucial factor:

* **Basic Concept:** Distance is a scalar quantity, meaning it only has magnitude and no direction. Unlike displacement, which considers direction, distance simply measures the "length" of the path traveled.
* **Real-life Examples:** Imagine walking from your house to a park 500 meters away. The distance you've traveled is 500 meters, regardless of the path taken.

In solving physics problems, it's essential to clearly identify the given distance so you can accurately apply it to formulas that involve speed and time.

Grasping Time in Motion

Time measures how long it takes for an event or action to occur. In the context of motion, time describes how long an object takes to move a certain distance. This is usually measured in seconds (s).

* **Key Role in Calculations:** In physics, time helps us understand the dynamics of motion. Knowing how much time it takes for an object to move a certain distance helps us uncover its speed.
* **Everyday Understanding:** Consider timing how long it takes you to drive to school. If it takes 5 minutes, you have measured the time for that motion.

When solving questions like the billiards problem, ensure you correctly use the time formula, \[ ext{time} = \frac{\text{distance}}{\text{speed}} \]. This precise use helps determine how long an object, like the ball in our exercise, takes to travel a set distance.

Decoding the Velocity Formula

At the heart of calculating motion is the velocity formula, which connects distance, velocity (or speed), and time. Although commonly referenced as speed when direction isn't a factor, velocity is key here.

* **Velocity vs. Speed:** Speed is a scalar quantity focused only on how fast something moves, whereas velocity is a vector including direction. In everyday scenarios, we often use speed to keep things simple.
* **Formula Basics:** The formula \[ ext{velocity} = \frac{ ext{distance}}{ ext{time}} \] can be rearranged to solve for any of its components. When distance and speed are known, the formula becomes \[ ext{time} = \frac{ ext{distance}}{ ext{speed}} \]. This is exactly how we approached solving the billiards exercise.

This equation is vital as it allows us to predict how fast an object will reach its destination or how long it will take to arrive, as seen in our exercise where we determine the time by dividing the distance by the speed of the ball.