Q: Problem 1

A car moving at ##25\text{ m/s}## decelerates uniformly at ##5\text{ m/s}^2## for ##4\text{ s}##. Find the final velocity.

Q: Problem 2

A bike slows from ##15\text{ m/s}## to ##3\text{ m/s}## in ##6\text{ s}##. Find the acceleration.

Q: Problem 3

A truck decelerates at ##2\text{ m/s}^2## from ##18\text{ m/s}##. How long until it stops?

Q: Problem 4

A train reduces speed from ##30\text{ m/s}## to ##10\text{ m/s}## in ##5\text{ s}##. Find the acceleration.

Q: Problem 5

A car moving at ##12\text{ m/s}## accelerates uniformly to ##20\text{ m/s}## in ##4\text{ s}##. Find the acceleration.

Question 1

Selecting the Appropriate Equation of Motion

Accepted Answer

To find the final velocity after a specific period of braking, we must choose from the primary equations of motion. These equations relate velocity, displacement, time, and acceleration in various combinations. The choice depends entirely on which variables are provided in the problem statement and which specific value we need to determine. Selecting the wrong formula can lead to unnecessary complexity or the need for extra data that is unavailable.

Question 2

Step-by-Step Computational Analysis

Accepted Answer

We begin the calculation by substituting the known numerical values into our selected kinematic formula. Substituting ##20## for the initial velocity ##u## and ##-4## for the acceleration ##a##, the equation takes a specific form:
###v = 20 + (-4 	imes 3)###
This clear substitution ensures that the negative nature of the deceleration is properly integrated into the summation. It prepares the equation for the final arithmetic steps.

Question 3

Problem 1

Accepted Answer

A car moving at ##25	ext{ m/s}## decelerates uniformly at ##5	ext{ m/s}^2## for ##4	ext{ s}##. Find the final velocity.

Question 4

Problem 2

Accepted Answer

A bike slows from ##15	ext{ m/s}## to ##3	ext{ m/s}## in ##6	ext{ s}##. Find the acceleration.

Question 5

Problem 3

Accepted Answer

A truck decelerates at ##2	ext{ m/s}^2## from ##18	ext{ m/s}##. How long until it stops?

Question 6

Problem 4

Accepted Answer

A train reduces speed from ##30	ext{ m/s}## to ##10	ext{ m/s}## in ##5	ext{ s}##. Find the acceleration.

Question 7

Problem 5

Accepted Answer

A car moving at ##12	ext{ m/s}## accelerates uniformly to ##20	ext{ m/s}## in ##4	ext{ s}##. Find the acceleration.

Question 8

Braking Efficiency and Road Safety

Accepted Answer

Understanding the final velocity after a specific braking duration is critical for modern automotive safety engineering. Engineers use these fundamental calculations to determine the baseline effectiveness of various braking system designs. Knowing how quickly a vehicle can shed speed helps in designing advanced collision avoidance systems and setting appropriate speed limits. This data is essential for ensuring that vehicles can respond safely to unexpected obstacles on the road.

Question 9

Energy Transformations in Friction Systems

Accepted Answer

Deceleration is not just a mathematical change in numbers; it represents a profound transformation of physical energy. As the car slows from ##20	ext{ m/s}## to ##8	ext{ m/s}##, its total kinetic energy is reduced significantly. According to the laws of thermodynamics, this energy cannot simply vanish but must be converted into another form. Understanding where this energy goes is a key aspect of mechanical and thermal engineering.

JUPITER SCIENCE

Final Velocity after Braking: Solving Kinematic Equations

Connected Bodies in Tension: Solving the Atwood Machine Problem

Understanding the Convergent Matrix

Understanding Linear and Circular Motion: Concepts and Applications

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