Variable acceleration with one premise

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SUMMARY

The particle's acceleration is defined by the equation a(t) = 2t + 1 m/s². To find the displacement from t = 2 to t = 4, one must first integrate the acceleration to derive the velocity function. The correct velocity function, derived from the acceleration, is v(t) = t² + t - 1, which satisfies the initial condition of v(2) = 5 m/s. The displacement can then be calculated by integrating the velocity function over the specified time interval.

PREREQUISITES
  • Understanding of calculus, specifically integration techniques.
  • Familiarity with kinematic equations in physics.
  • Knowledge of initial conditions in motion problems.
  • Basic understanding of units of measurement, specifically meters per second (m/s).
NEXT STEPS
  • Learn integration techniques for deriving velocity from acceleration functions.
  • Study kinematic equations and their applications in physics problems.
  • Explore the concept of initial conditions and their importance in motion equations.
  • Review unit conversions and their relevance in physics calculations.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and motion, as well as educators looking for examples of integration in kinematics.

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Homework Statement



A particle's acceleration is given by the equation a(t) = 2t + 1 m/seg^2. If its velocity at t = 2 equals 5 m/seg, how much does its displacement change from t = 2 to t = 4?

Homework Equations





The Attempt at a Solution



I thought I could integrate the acceleration equation to get the velocity equation, but when I solve this equation for t = 2, I don't get 5 m/seg as the problem states. Here's the equation I came up with:

v(t) = t^2 + t

Should I add a -1 to the end so the equation satisfies the premise?
 
Physics news on Phys.org
What is seg?
 
Abdul Quadeer said:
What is seg?

I'm sorry, second.
 

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