How large a net force is required to accelerate a 1600-kg SUV from rest to a speed of 25 m/s in a distance of 200 m?

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Solution:

Given,

Mass = m = 1600 Kg

Initial Speed = u = 0 m/s

Final Speed = v = 25 m/s

Distance = d = 200 m

Net Force = F = ?

 

Formula used,   F*d = Change in Kinetic Energy 

                          F*d = Final Kinetic Energy - Initial Kinetic Energy

                          F*d = $\frac{1}{2}m(v^2 - u^2)$

Placing values in the equation,

                    F*200 = $\frac{1}{2}1600((25)^2 - 0^2)$

                    F*200 =  800*625

                            F = $\frac{5*10^5}{200}$

                            F = 2500 N 

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