Calculus Problem: acceleration, speed, and displacement of a particle

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SUMMARY

The discussion focuses on solving a calculus problem involving the acceleration of a particle defined by the equation a = A√t, where A = 2.0 m/s5/2. The initial conditions are given as v(0) = 7.5 m/s and x(0) = 0. Participants provide insights on integrating the acceleration to find speed and displacement as functions of time, emphasizing the use of definite integrals in physics. The key equations involve integrating acceleration to derive velocity and position functions.

PREREQUISITES
  • Understanding of calculus, specifically integration techniques.
  • Familiarity with the concepts of acceleration, velocity, and displacement in physics.
  • Knowledge of definite integrals and their application in physics problems.
  • Basic understanding of particle motion and kinematics.
NEXT STEPS
  • Study the process of integrating acceleration to derive velocity functions.
  • Learn how to apply definite integrals in physics problems involving motion.
  • Explore the relationship between acceleration, velocity, and displacement in kinematics.
  • Practice solving similar problems involving variable acceleration and initial conditions.
USEFUL FOR

Students studying calculus and physics, particularly those tackling problems related to particle motion and integration techniques. This discussion is beneficial for anyone looking to deepen their understanding of the relationship between acceleration, speed, and displacement.

Stephanievet54
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Homework Statement


The acceleration of a particle given a=A√t where A=2.0 m/s5/2. At t=0, v=7.5 m/s and x=0. (a) What is the speed as a function of time? (b) What is the displacement as a function of time? (c) What are the acceleration, speed, and displacement at t=5.0s.

Homework Equations

The Attempt at a Solution


I tried to integrate a=A√t, but I don't know where to plug in v and x. Any help will be greatly appreciated.
 
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Hi Stephanievet54 and welcome to PF.

Can you show in detail what you tried to do? Remember that in physics you deal with definite integrals. For example, if ##a=\frac{dv}{dt}##, then $$\int_{v_0}^v dv=\int_{t_0}^{t}a(t') dt'$$Note that at the lower limit of time ##t_0## the velocity is ##v_0## and at the upper limit of arbitrary time ##t## the velocity is ##v##. The integration on the right is over dummy variable ##t'##. Similar considerations apply for ##x(t)##.
 
Last edited:

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