Understanding Acceleration: Calculating Time and Distance for a Car

When analyzing motion, one of the fundamental principles is the application of acceleration, which measures the rate of change of velocity. In this article, we will explore how to calculate the time required for a car to reach a specific velocity and the distance it covers. We will use a practical example to clarify the concepts and provide a detailed solution.

Example Scenario

Consider a car that has an acceleration of 6 MS-2. Starting from rest, we need to determine the time it will take for the car to reach a velocity of 48 m/s and the distance it will cover during this period.

Time to Reach Velocity of 48 m/s

To calculate the time it takes for the car to reach a velocity of 48 m/s, we can use the formula for constant acceleration:

v u at

Where:

v is the final velocity (48 m/s) u is the initial velocity (0 m/s since the car starts from rest) a is the acceleration (6 m/s2) t is the time

Step-by-Step Solution

Substituting the known values into the equation:

48 0 6t

Therefore:

48 6t

Dividing both sides by 6, we get:

t 8 seconds

This means it will take the car 8 seconds to reach a velocity of 48 m/s.

Distance Covered during the Period

Now, let's calculate the distance the car covers during this period. We can use the third equation of motion:

v2 u2 2as

Where:

v is the final velocity (48 m/s) u is the initial velocity (0 m/s) a is the acceleration (6 m/s2) s is the distance

Step-by-Step Solution

Substituting the known values into the equation:

482 02 2 × 6 × s

Therefore:

2304 12s

Dividing both sides by 12, we get:

s 192 meters

Thus, the car covers a distance of 192 meters during the 8 seconds.

Conclusion

In this article, we have explored a practical example demonstrating how to calculate the time and distance covered by a car under constant acceleration. By using basic principles of motion, we were able to determine that the car will take 8 seconds to reach 48 m/s and will cover a distance of 192 meters during this period.

Understanding these concepts can be crucial in various fields, from automotive engineering to sports analysis. If you need further clarification or have additional questions, feel free to explore our detailed solutions or visit the link for more information.