Posted by Phil on Sunday, October 2, 2011 at 12:25pm.
First calculate the required acceleration, a, with suitable units of m/s^2.
Vfinal = 64 km/h = 17.78 m/s
Vfinal = sqrt(2 a X)
a = (Vfinal)^2/(2X) = 2.11 m/s^2
Then use Newton's second law, along the direction of motion. If the pushing force is F, the net force in the direction of motion is
Fnet = F + M*g sin6 -M*g*cos6*0.15
= M a
Use that equation to solve for F.
You could also use a conservation of energy method. (Work applied) = F*X
= PE loss + KE gain + (work against friction)
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