Solving for Distance and Time: Motion on Incline Homework Help

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SUMMARY

The discussion focuses on solving a physics problem involving a ball rolling down an inclined plane, specifically determining the distances marked at intervals of 1.6 seconds. The key equation used is x = kt², where k is a constant derived from the known distance of 1.4 meters at 3.2 seconds. The value of k is calculated to be 0.55, which is then used to find the distance for the first mark. The participants confirm that the ball rolls with constant acceleration, validating the use of the equation.

PREREQUISITES
  • Understanding of kinematics, specifically motion with constant acceleration
  • Familiarity with the equation of motion: x = kt²
  • Basic algebra skills for solving equations
  • Knowledge of time intervals in physics problems
NEXT STEPS
  • Learn how to derive the constant k in motion equations
  • Study the principles of constant acceleration in physics
  • Explore more complex kinematic equations and their applications
  • Practice solving similar problems involving inclined planes and rolling objects
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Students studying physics, particularly those focusing on kinematics and motion, as well as educators looking for examples of inclined plane problems.

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Homework Statement




A ball is allowed to roll from rest down an inclined plane, and the distances are marked every 1.6 s. If the second mark is made 1.4 m from the starting point, where is the first mark?

Where is the Fourth Mark?

Homework Equations



x=kt^2 .. k is the constant that I need to figure out to answer the questions.

t = 4 x 1.6s for the 2nd part of the question

The Attempt at a Solution



I'm confused with what variables to plug in in order to answer the question.

t is obviously 1.6s, but I don't know the X.
1.4 = k1.6^2 = 1.4 = k2.56 ... 1.4 / 2.56 = k .. 0.55 = k .. Not correct. I need this K in order to find the solution to the 2nd problem
 
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Welcome to PF!

I think the ball will roll with constant acceleration so your x = kt² should be right. Very clever of you to see that, or guess it.

You are interested in two sets of data:
1) d = ?, t = 1.6
2) d = 1.4, t = 3.2
In the second one, you know both d and t so you can plug them into the formula and find the k. Then apply the formula with the known value of k to the first set to find its d.
 
Thanks for the help Delphi! :) (Sorry for my lateness, but wanted to show my gratitude)
 

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