Question

An SUV drives on a straight-line track. Starting with a speed v=20.7 m/s, it comes to rest over a distance d=39.9 m. a 50%

(a) Write an expression for the magnitude of the net force on a passenger with mass m. as 50%

Answer 1

The magnitude of the net force on a passenger with mass F= mv^2/2d.

The expression for the magnitude of the net force acting on a passenger with mass m can be derived using the work-energy principle. When an SUV comes to rest, the work done by the net force is equal to the initial kinetic energy of the system. The work done (W) is given by W= 1/2mv^2, where v is the initial velocity.

In this case, the work done is also equal to the force (F) multiplied by the displacement (d), i.e., W=Fd. Equating the two expressions for work done, we get Fd= 1/2 mv^2. Solving for the force (F), we find F= mv^2/2d. This formula represents the magnitude of the net force acting on the passenger as the SUV decelerates to rest over a distance d with an initial speed v.