An experimental rail car with a rocket mounted on it is free to slide on a rail that is so slippery it can be considered to be frictionless. The force that the rocket exerts on the car is given by: F(x)= Ax2N, 0396m where x is the position along the rail and A = 18.5. The mass of the rail car is 6390 kg. The rail car starts from rest. (a) What are the units of A? (b) What is the total work done on the rail car by the rocket in the first 448 m of travel? (answer: 4.98 x 107 J) (c) What is the speed of the rail car after the first 448 m of travel? (answer: 125 m/s)
An experimental rail car with a rocket mounted on it is free to slide on a rail that is so slippery it can be considered to be frictionless. The force that the rocket exerts on the car is given by:
F(x)= Ax2N, 0<x<127m
1.38x105 N, 127<x<396m
0, x>396m
where x is the position along the rail and A = 18.5. The mass of the rail car is 6390 kg. The rail car starts from rest.
(a) What are the units of A?
(b) What is the total work done on the rail car by the rocket in the first 448 m of travel? (answer: 4.98 x 107 J)
(c) What is the speed of the rail car after the first 448 m of travel? (answer: 125 m/s)
(d) Show that the rate of change of kinetic energy (K) of an object at a particular moment is given by dK/dt = Fv, where F is the net force exerted on the object at that particular moment and v is the speed of the object at that particular moment.
(e) Calculate the rate of change of the rail car’s kinetic energy at x = 123 m. (answer: 1.68 x 107 J/s)
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