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LippyKa16
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Homework Statement
A car is traveling up a slope. Given that a(t) is constant at 1m/s^2, find the expression of motor power in time. Assuming that the maximum power of the car is 215kW, for how long can the car maintain such an acceleration?
Mass of car (m) = 2000 kg
The hill has a constant inclination of 8 degrees (Θ = 8)
Initial velocity (u) = 90 km/h or 25 m/s
Friction coefficient due to wheel contact is 0.1
Air resistance (F[air]) = 0.85*v^2
Velocity = v, Time = t, Height = h, Force = F, Power = P
Energy = E, Kinetic Energy = KE, Gravitational Potential Energy = GPE
Homework Equations
P = ∑F * v
P = dE/dt
E = KE + GPE (no elastic potential energy)
GPE = 1/2*m*(h[final] - h[initial])
h[final] = s * sinΘ (s = distance)
s = 1/2(u+v)t (SUVAT equation)
The Attempt at a Solution
I drew a free body diagram of the system with a rotated axis so that the Normal force was the only force that was at an angle.
P[air] = F[air] * v * cosΘ * cos180
P[air] = -0.84*v^3
P[friction] = F[friction] * v * cosΘ * cos180 (F[friction] ~ 1942.91 N)
P[friction] = -1924.00*v
Assuming P[max] = P[motor]...
215,000 - 0.84*v^3 - 1924*v = dKE/dt + dGPE/dt
Maximum velocity means acceleration = 0
Maximum velocity also means KE = 0
Assuming h[initial] = 0
215,000 - 0.84*v^3 - 1924*v = d/dt (1/2*m*(1/2(u+v)t * sinΘ))
215,000 - 0.84*v^3 - 1924*v = d/dt(1000[(12.5t + 0.5vt)sinΘ])
I am stuck here because I think I am on the wrong track.
Any help is greatly appreciated.