The kinetic energy KE of an object of mass m moving with velocity v is defined as KE -m2. If a force fx) acts on the object, moving it along the x-axis from xi to x2, the Work-Energy Theorem states that the net weight equal to the change in kinetic energy: mv2 - mv1, where V1 is the velocity at xi and v2 is the velocity at x2. Suppose that when launching a 700-kg roller coaster car an electromagnetic propulsion system exerts a force of 5.7x2 + 1.5x newtons on the car at a distance x meters along the track. Use the Work-Energy Theorem to find the speed of the car when it has traveled 60 meters.

v = 34.35 m/s

Explanation:

In order to find the speed of the car, when it has traveled 60m, you take into account the Work-Energy theorem, which is given by the following formula:

    (1)

W: work done on the roller coaster by the electromagnetic propulsion

m. mass of the roller coaster = 700kg

v2: final speed of the roller coaster = ?

v1: initial speed = 0m/s

you have that the force exerted on the roller depends on x, the distance traveled by the roller. To calculate the work W, you use the following integral:

       (2)

where F is given by:

You replace the previous function F in the integral (2) and calculate W:

Next, you solve the equation (1) for v2, and replace the values of all parameters:

The final speed of roller coaster, after it has traveled 60m is 34.35m/s

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