How Is the Distance of 262m Calculated for a Particle Accelerating from Rest?

Click For Summary
SUMMARY

The distance of 262 meters for a particle accelerating from rest over 20 seconds is calculated using kinematic equations. The particle accelerates at 2 m/s² for the first 10 seconds, remains at constant velocity for the next 5 seconds, and then decelerates at -3 m/s² for the final 5 seconds. The solution involves applying the equations of motion for each segment of the particle's movement to derive the total distance traveled.

PREREQUISITES
  • Understanding of kinematic equations
  • Knowledge of acceleration and deceleration concepts
  • Ability to interpret motion graphs
  • Familiarity with basic physics principles
NEXT STEPS
  • Review the kinematic equations for uniformly accelerated motion
  • Learn how to calculate distance using initial velocity, acceleration, and time
  • Study the concept of piecewise motion in physics
  • Explore graphical analysis of motion and its implications
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and motion analysis, as well as educators looking for examples of problem-solving in particle dynamics.

profcocoon
Messages
1
Reaction score
0

Homework Statement



A particle moves from a rest position and accelerates as shown in the graph, which is the distance that the particle has advanced during the first 20 seconds?


Homework Equations





The Attempt at a Solution



The answer in the book is 262m but I have no idea of how that solution was obtained, could you guys help me??
 

Attachments

Physics news on Phys.org
profcocoon said:

Homework Statement



A particle moves from a rest position and accelerates as shown in the graph, which is the distance that the particle has advanced during the first 20 seconds?


Homework Equations





The Attempt at a Solution



The answer in the book is 262m but I have no idea of how that solution was obtained, could you guys help me??
Profcocoon, welcome to PF!

From your graph, the acceleration appears to be 2 m/s^2 for the first 10 seconds; then there is no acceleration for the next 5 seconds; and then it accelerates at -3 m/s^2 in the final 5 seconds.

Please list what you think are the relevant equations, and show some attempt at a solution using the relevant kinematic equations over the different time periods. You must show some attempt before we can be of further assistance.
 

Similar threads

Voltage that gives acceleration to relativistic particles
  • · Replies 3 ·
Replies
3
Views
717
Acceleration straight line graph
  • · Replies 3 ·
Replies
3
Views
6K
Closest distance of approach between 2 charged particles
  • · Replies 5 ·
Replies
5
Views
2K
Given an acceleration figure calculate speed and distance
  • · Replies 1 ·
Replies
1
Views
3K
Particle Motion; Acceleration directly proportional to time
  • · Replies 2 ·
Replies
2
Views
5K
Relating acceleration to distance and time
  • · Replies 5 ·
Replies
5
Views
3K
Synchrotron Particle Accelerator: How Does It Work?
  • · Replies 25 ·
Replies
25
Views
5K
Problem with the power of car
  • · Replies 3 ·
Replies
3
Views
1K
Plot the position of the particle x=Acosbt
  • · Replies 3 ·
Replies
3
Views
2K
Find the minimum distance between 2 particles
  • · Replies 4 ·
Replies
4
Views
6K