Understanding Acceleration and Distance Covered by a Car Moving at a Constant Rate

Understanding the fundamental principles of physics, particularly those governing the motion of vehicles, is crucial for many applications in engineering, transportation, and even everyday life. This article delves into the concepts of acceleration and distance covered by a car as it increases its speed. We will calculate the acceleration and distance traveled using the known initial and final speeds, along with the time interval during which the speed change occurs.

Initial and Final Speeds

Let's consider a car that is initially moving at a speed of 36 km/h. This speed can be converted from kilometers per hour to meters per second (m/s) using the conversion factor 1 km/h 1000 m / 3600 s. Therefore:

36 km/h 36 3.6 10 m/s

The car then increases its speed to 54 km/h, which we convert to m/s in a similar manner:

54 km/h 54 3.6 15 m/s

Calculating Acceleration

Acceleration is the rate of change of velocity with respect to time. In this case, the acceleration can be calculated as follows:

a v - u t 15 - 10 10 0.5 m /s

The acceleration of the car is 0.5 m/s2.

Calculating the Distance Covered

Using the basic kinematic equation for uniformly accelerated motion, we can calculate the distance covered by the car during the 10-second interval:

s v 2 - u 2 2 a 15 2 - 10 2 2 × 0.5 125 m

The distance covered by the car in this 10-second interval is 125 meters.

Conclusion

Understanding the principles of acceleration and distance covered is vital for any analysis involving the motion of vehicles. In this article, we have demonstrated the process of calculating both the acceleration and the distance covered by a car that increases its speed from 36 km/h to 54 km/h over a period of 10 seconds. These calculations can be applied to real-world scenarios, such as traffic management, engineering design, and the evaluation of the efficiency of transportation systems.

Frequently Asked Questions

Q: How do you convert km/h to m/s?

A: To convert kilometers per hour (km/h) to meters per second (m/s), you can use the conversion factor 1 km/h 1000 m / 3600 s. This is often simplified to 1 km/h 5/18 m/s. Therefore, to convert 36 km/h to m/s:

36 km/h 36 1.852 10 m/s

Q: What formula is used to calculate acceleration?

A: The formula for acceleration is:

a v - u t

Where v is the final velocity, u is the initial velocity, and t is the time interval.

Q: How do you find the distance covered under uniform acceleration?

A: The distance covered under uniform acceleration can be calculated using the formula:

s v 2 - u 2 2 a

Where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance covered.