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## Homework Statement

A 2000 kg car is driving up a 20° grade at a speed of 85 km/h. What force must be applied to the car to accelerate it up to 100 km/h in 10s?

m= 2000 kg

θ= 20°

V

_{o}= 85 km/hr = 23.6 m/s

V

_{f}= 100 km/hr = 27.8 m/s

t = 10 s

## Homework Equations

F = ma (F

_{x}= ma

_{x})

F

_{x}= Fcosθ

V

_{ox}= V

_{o}cosθ

V

_{oy}= V

_{o}sinθ

V

_{x}= V

_{ox}+ a

_{x}t

V

_{x}= V

_{ox}+a

_{x}t

## The Attempt at a Solution

I found these using the cos or sin equations above:

V

_{ox}= 22.1 m/s

V

_{oy}= 8.07 m/s

V

_{x}= 26.1 m/s

V

_{y}= 9.51 m/s

Using the last equation, I found a

_{x}= 0.4 m/s

^{2}

F

_{x}= 800 N

I then solved for F using the second equation by dividing F

_{x}by cosθ, making F= 851 N. I think I did something wrong when I solved for a, and my guess is that I couldn't use 10s for that since it was the incline, when I used it for the x values. I'm stuck on how to fix it, or on how to solve the problem a different way. These are practice problems that I have the answers to, but no solutions, so I know that F=7.5 kN.

I tried working backward and got that a=3.75 m/s

^{2}and a

_{x}=3.52 m/s

^{2}. Using F=ma and the cos, I got F

_{x}= 7040 N, which gets me the right answer however I do it. This makes me fairly certain that I'm doing something wrong with getting the acceleration.

Thanks in advance!