Calculating Final Speed, Average Speed, and Distance Traveled for a Decelerating Car

Understanding the motion of objects, particularly when they are decelerating, is crucial in many real-world applications. This article will walk you through the process of calculating the final speed, average speed, and distance traveled for a car that is decelerating uniformly.

Problem Statement

A car is moving at a uniform speed of 40 m/s and then decreases its speed uniformly at a rate of 5 m/s2. We need to find its speed after 6 seconds, the average speed during this duration, and the distance traveled in these 6 seconds.

Equations of Motion

For uniformly decelerated motion, we can use the following equations of motion:

1. Final Speed (v):

The formula for the final speed is:

(v u at)

Where:

u initial speed (40 m/s) a acceleration due to deceleration (-5 m/s2 because it's a decrease in speed) t time (6 seconds)

Substituting the values:

(v 40 , text{m/s} (-5 , text{m/s}^2) times 6 , text{s})

(v 40 , text{m/s} - 30 , text{m/s})

(v 10 , text{m/s})

2. Average Speed (vavg):

The formula for the average speed is:

(v_{avg} frac{u v}{2})

Where:

u initial speed (40 m/s) v final speed (10 m/s)

Substituting the values:

(v_{avg} frac{40 , text{m/s} 10 , text{m/s}}{2})

(v_{avg} frac{50 , text{m/s}}{2} 25 , text{m/s})

3. Distance Traveled (d):

The formula for the distance traveled is:

(d ut frac{1}{2}at^2)

Where:

u initial speed (40 m/s) a acceleration (deceleration, -5 m/s2) t time (6 seconds)

Substituting the values:

(d 40 , text{m/s} times 6 , text{s} frac{1}{2}(-5 , text{m/s}^2) times (6 , text{s})^2)

(d 240 , text{m} frac{1}{2}(-5) times 36)

(d 240 , text{m} - 90 , text{m} 150 , text{m})

Summary

After 6 seconds, the car's speed is:

Final Speed: 10 m/s

The car's average speed during this time is:

Average Speed: 25 m/s

The distance traveled after 6 seconds is:

Distance Traveled: 150 m

Formulas Recap

For a car decelerating uniformly:

Final Speed (v):

(v u at)

Average Speed (vavg):

(v_{avg} frac{u v}{2})

Distance Traveled (d):

(d ut frac{1}{2}at^2)

By memorizing these formulas, you can easily solve similar problems in physics and engineering.

Final Equations

Vf: (v u at) Vavg: (v_{avg} frac{u v}{2}) S: (d ut frac{1}{2}at^2)

Remembering these equations and their application will help you tackle various motion-related problems more efficiently.