Calculus based kinematics problem.

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SUMMARY

The discussion centers on a calculus-based kinematics problem involving a trolley released from rest on an 8-meter runway, with its displacement described by the equation s = 2t + t². The participants successfully derived the velocity by differentiating the displacement expression once and the acceleration by differentiating it twice. They also clarified that to find the time taken to reach the bottom of the runway and the velocity at that point, one can set the displacement equation equal to 8 meters and solve for t.

PREREQUISITES
  • Understanding of calculus differentiation
  • Familiarity with kinematic equations
  • Basic knowledge of motion concepts (displacement, velocity, acceleration)
  • Ability to solve quadratic equations
NEXT STEPS
  • Practice differentiating polynomial functions to find velocity and acceleration
  • Explore solving quadratic equations for time in motion problems
  • Learn about the relationship between displacement, velocity, and acceleration in kinematics
  • Study real-world applications of calculus in physics problems
USEFUL FOR

Students studying physics or calculus, particularly those focusing on kinematics and motion analysis. This discussion is beneficial for anyone looking to strengthen their understanding of the application of calculus in solving real-world motion problems.

Phlebas
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Homework Statement


A trolley is released from rest from the top of a runway which is 8m long. The displacement, s in metres, of the trolley is given by the expression(see below) where t is in seconds. Using calculus initially determine (a) an expression for the velocity of the trolley (b) the acceleration of the trolley (c) the time it takes the trolley to reach the bottom of the runway (d) the velocity of the trolley at the bottom of the runway.


Homework Equations


s=2t+t2


The Attempt at a Solution


So I differentiated the displacement expression once to get a velocity expression and twice to get an acceleration expression. Can't quite figure out how to do (c) or (d) though, as my calculus is pretty rusty.
 
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You have an expression for displacement in terms of t (time). You know the length of the runway, therefore you can find the time it takes to travel down said runway, yes?
 
slip of the brain. I get it now.
 

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