Acceleration Problem: Calculating Time Difference for Porsche vs. Honda 400 Race

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In a race between a Porsche with an acceleration of 3.5 and a Honda with an acceleration of 3.0, the Honda starts with a 50-meter head start. To calculate the time difference for the winner, the formula x = v_0t + 1/2 at^2 is recommended for both vehicles. The key unknown in this equation is time, which needs to be solved for each car to determine the winner. Previous attempts at calculating the time difference yielded various results, but the correct approach involves comparing the times derived from the formula. Ultimately, the discussion emphasizes the importance of accurately applying the physics formula to find the winning time difference.
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A Porsche challenges a Honda to a 400 race. Because the Porsche's acceleration of 3.5 is larger than the Honda's 3.0 , the Honda gets a 50 head start. Assume, somewhat unrealistically, that both cars can maintain these accelerations the entire distance.

By how much time does the winner win?
 
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What have you tried?
 
Pretty much everything I could think of. We have online homework and we have to submit the answer and we only have 6 attempts.. and I'm down to two. The answers I have submitted already are: 2.39, 1.5, .85, and .11
 
Well if you're using this formula:

x = v_0t + \frac{1}{2}at^2

Then, you should get the right answer. The only unknown in that formula is the time, which is what you are after. Simply do that for both cars and compare their times.
 
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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