How Do You Calculate Stopping Distance on a Slope?

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To calculate the stopping distance of a car traveling up a 15-degree slope at 35.0 m/s with a kinetic friction coefficient of 0.800, the acceleration must first be determined. The user is attempting to find stopping distance using the equation x = x0 + v0t + (1/2)at^2, which is a valid approach. Another suggested method involves using the formula v^2 = u^2 + 2as, which can also yield the stopping distance. The discussion emphasizes the importance of correctly calculating acceleration before applying these equations. Ultimately, both methods can lead to the correct stopping distance if applied properly.
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Problem:
A car is traveling up a 15 degree slope at a speed of 35.0 m/s when the driver slams on the brakes and skids to a halt. The coefficient of kinetic friction between the tires and road is 0.800. Find the cars acceleration and the stopping distance.

I found the acceleration and was trying to the find the stopping distance using x=xo + voxt+ axt^2/2. I don't know if this is the right approach.
 
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This is how I would solve for the stopping distance. I think you are on the right track. Continue working and see if you get the right answer. If not, then we are here.:smile:
 
I suppose you could use v^2=u^2+2as
 
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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