Time for Non-Uniform Acceleration

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SUMMARY

The discussion focuses on calculating the time taken for a vehicle to travel 200 feet under non-constant acceleration of 32.17 m/s². The user recognizes that traditional kinematics cannot be applied due to the variable acceleration and suggests the need for calculus and differential equations. Key points include the acknowledgment of initial conditions (x1=0, x2=200, a1=0, a2=32.17) and the challenge of determining the relationship between acceleration and displacement or time. The user seeks clarification on how to approach the problem without a defined function.

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  • Understanding of calculus and differential equations
  • Familiarity with concepts of acceleration and velocity
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  • Basic principles of motion under variable acceleration
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I've been trying to figure out this seemingly simple problem for a theoretical project I'm doing, but can't figure it out.

Homework Statement


This isn't real, but say that a vehicle travels from 0 to 200 feet linearly at a non-constant acceleration of 32.17 m/s^2 (1g), but the acceleration is in a linear y=mx line. Ignoring friction forces, how long did it take to travel that 200 feet?

Homework Equations



The Attempt at a Solution


I know I can't use kinematics because it's a non-constant acceleration, so I'll probably have to use calculus and differential equations. I know that the graph of velocity will be exponential, and acceleration will be linear. I don't know any times so I can't take the integral.

I know: x1=0, x2=200, a1=0, a2=32.17, but that's about it.

Any ideas on how I can tackle this problem without a function?
 
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I think it might help if you stated the problem. The acceleration varies linearly with what? displacement ? time? If a1 is zero why will the body start moving? Does it have a velocity?
 

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