Max Acceleration in Linearly Varying Speed: Solving for a0 and K

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The discussion focuses on determining the maximum acceleration of a vehicle that accelerates from rest to specified speeds under the assumption of linearly varying acceleration. The equation a(v) = a0 + Kv is central to the problem, where a0 represents the initial acceleration and K is a constant. The user is prompted to apply the relationship dv/dt = a0 + Kv to solve for the maximum acceleration at the given speeds of 50 mph and 65 mph. The conversation emphasizes the need to integrate the acceleration function to find the maximum values. Ultimately, the goal is to accurately calculate the maximum acceleration for both scenarios.
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Homework Statement


The driver of a vehicle on a level road determined that she could increase her speed from rest to 50 mph in 35 sec and from rest to 65 mph in 95 sec. Assume that acceleration varies linearly with speed (with a non zero intercept). Determine the max acceleration in each case.


Homework Equations



a(v) = a0 + Kv

The Attempt at a Solution



a(0) = a0
a(vmax) = amax
 
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Ok, so a(v)=dv/dt. You forgot that equation. Can you solve dv/dt=a0+Kv?
 

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