Question

An amusement park is creating signs to indicate the velocity of a roller coaster car on certain hills of the most popular ride. A roller coaster gains kinetic energy as itgoes down a hill. The velocity of an object in kilometers per hour (kph) can be determined by V where is the kinetic energy of the object in joules (1)and is the mass of the object in kilograms(kg)A roller coaster car has a mass of 450 kg and the car has a kinetic energy of 22,500 J on the first hill What velocity does the car obtain on the first hill?

Answer 1

Take into account that the kinetic energy of an object with speed v is given by the following formula:

K = 1/2 Mv²

where m is the mass and v the speed.

M = 450 kg

v = ?

K = 2,500 J

solve for v the previous formula and replace the values of the parameters, just as follow:

K = 1/2 Mv² multiply by 2 both sides

2K = Mv² divide by m

2K/m = v² apply square root both sides

√(2K/M) = v

then, you have

v = √(2(22,500 J)/450kg)

v = 10 m/s

Hence, the speed of the object is 10 m/s