Motorcycle Kinematics Problem Solving Time To Cover 46 Meters

by ADMIN 62 views

A motorcycle starts from rest, and in two consecutive seconds it travels 20 m and 30 m. Find the time in seconds when it travels a distance of 46 m.

Introduction

In this article, we delve into the fascinating realm of kinematics, the branch of physics that deals with the motion of objects without considering the forces that cause the motion. Our focus is on a specific scenario involving a motorcycle accelerating from rest. We will analyze the motorcycle's motion to determine the time it takes to cover a distance of 46 meters, given that it travels 20 meters in the first two seconds and 30 meters in the subsequent two seconds. This problem exemplifies the application of fundamental kinematic principles and equations, offering a practical understanding of how objects move under constant acceleration.

To solve this problem effectively, we'll employ the following key kinematic concepts and equations:

  1. Uniform Acceleration: We'll assume that the motorcycle's acceleration is constant throughout its motion. This assumption allows us to use the standard kinematic equations.
  2. Displacement: The change in position of the motorcycle, measured in meters.
  3. Initial Velocity: The motorcycle's velocity at the beginning of its motion (which is zero in this case, as it starts from rest).
  4. Final Velocity: The motorcycle's velocity at a specific point in time.
  5. Time: The duration of the motion, measured in seconds.
  6. Kinematic Equations: We'll utilize the following equations:
    • d = v₀t + (1/2)at² (where d is displacement, v₀ is initial velocity, t is time, and a is acceleration)
    • v = v₀ + at (where v is final velocity)

By carefully applying these concepts and equations, we can dissect the motorcycle's motion and accurately determine the time required to cover 46 meters.

Problem Statement

A motorcycle starts from rest. During two consecutive seconds, it covers 20 meters and then 30 meters. The challenge is to determine the time at which the motorcycle covers a total distance of 46 meters from its starting point. This problem requires a detailed analysis of the motorcycle's motion, particularly its acceleration and how the distance covered changes over time.

Breaking Down the Problem

To solve this, we need to break the problem down into manageable steps:

  1. Identify the Knowns: List the given information, such as the distances covered in specific time intervals and the initial condition of the motorcycle being at rest.
  2. Determine the Unknowns: Pinpoint what we need to find, which is the time taken to cover 46 meters.
  3. Establish a Strategy: Formulate a plan using the kinematic equations to relate the knowns and unknowns.
  4. Solve for Acceleration: Use the information about the distances covered in the first two time intervals to calculate the motorcycle's acceleration.
  5. Calculate the Time: Once we have the acceleration, we can use the kinematic equations to find the time taken to cover 46 meters.

By following this structured approach, we can systematically solve the problem and gain a deeper understanding of the motorcycle's motion.

Solution

Step 1: Defining Variables and Knowns

Let's start by defining the variables and knowns:

  • t₀ = 0 s (initial time)
  • v₀ = 0 m/s (initial velocity, since the motorcycle starts from rest)
  • Δt₁ = 2 s (first time interval)
  • Δd₁ = 20 m (distance covered in the first time interval)
  • Δt₂ = 2 s (second time interval)
  • Δd₂ = 30 m (distance covered in the second time interval)
  • d = 46 m (total distance to be covered)
  • a = acceleration (constant, to be determined)
  • t = time to cover 46 m (to be determined)

Step 2: Calculating Acceleration

We can use the kinematic equation for displacement under constant acceleration to find the acceleration. The equation is:

Δd = v₀Δt + (1/2)a(Δt)²

First, let's consider the first 2 seconds:

20 m = (0 m/s)(2 s) + (1/2)a(2 s)²

20 m = 0 + 2a s²

a = 10 m/s²

Now, we have the acceleration, a = 10 m/s². This is a crucial piece of information that will help us determine the time taken to cover 46 meters.

Step 3: Determining the Time to Cover 46 Meters

Now that we know the acceleration, we can use the same kinematic equation to find the time t it takes to cover 46 meters. The equation is:

d = v₀t + (1/2)at²

Plugging in the values:

46 m = (0 m/s)t + (1/2)(10 m/s²)t²

46 m = 5t² m/s²

t² = 46 m / (5 m/s²)

t² = 9.2 s²

Taking the square root of both sides:

t = √9.2 s²

t ≈ 3.03 s

Therefore, it takes approximately 3.03 seconds for the motorcycle to cover 46 meters from its starting point.

Conclusion

In conclusion, by applying the principles of kinematics and utilizing the equations of motion under constant acceleration, we have successfully determined that it takes approximately 3.03 seconds for the motorcycle to cover a distance of 46 meters from rest. This problem highlights the importance of understanding and applying fundamental physics concepts to solve real-world scenarios. The structured approach we followed, from defining variables and knowns to calculating acceleration and finally determining the time, underscores the methodical nature of physics problem-solving.

This analysis not only provides a specific answer to the problem but also demonstrates the power of kinematics in predicting and understanding the motion of objects. The same principles and methods can be applied to a wide range of problems involving moving objects, making this a valuable exercise in physics education and practical application.

Keywords

Motorcycle kinematic analysis: The article analyzes the motion of a motorcycle, applying principles of kinematics to determine the time it takes to cover a specific distance.

SEO Title

Motorcycle Kinematics Problem Solving Time to Cover 46 Meters