How Do You Model a Car's Decreasing Acceleration Mathematically?

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The discussion focuses on modeling a sports car's decreasing acceleration mathematically, with specific parameters provided. The car accelerates from rest to 40 m/s over 200 m, with a maximum acceleration of 10.4 m/s². Participants emphasize the need to show work for clarity and suggest starting with a visual representation of the problem. The concept of decreasing linear acceleration is explored, proposing an equation where acceleration decreases from an initial value over time. Clear equations for acceleration, velocity, and position as functions of time are essential for solving the problem effectively.
hmcaldwell01
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HELP! Physics problem due tomorrow!

Homework Statement



A sports car can accelerate from rest to a speed of 40 m/s while traveling a distance of 200 m. Assume the acceleration of the car can be modeled as a decreasing linear function of time, with a maximum acceleration of 10.4 m/s^2. I must write equations for the acceleration, velocity and position of the car as functions of time.

Homework Equations





The Attempt at a Solution


 
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Hi hmcaldwell01, Welcome to the Physics Forum.

While we can appreciate the urgency of your request, we can't help if you don't show any work.

It would be good to start with a picture of things and then attempt to write equations to stop the problem.

what does it mean to say the acceleration is a decreasing linear function? Does that mean the acceleration starts at 10.4 m/s^2 and then drops down to zero like the equation:

a= a_initial - k * t where k is to be determined
 
Last edited:
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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