(a) What is the final velocity of a car originally traveling at 50.0 km/h that decelerates at a rate of 0.400 m/s2 for 50.0 s?
(b) What is unreasonable about the result?
(c) Which premise is unreasonable, or which premises are inconsistent?
(a) The final velocity is (-6.11) m/s.
(b) It is unreasonable that on the application of brakes, the car will move in the opposite direction.
(c) The unreasonable premise is that the car traveling at a speed of 13.89 m/s can decelerate at a rate of 0.4 m/s2 in 50 seconds.
Apply the following equation of motion as:
Here, v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Convert the initial speed of the car from 50.0 km/h to m/s as:
Substitute 13.89 m/s for u, (-0.4) m/s2 for a, and 50 s for t in the above expression, and we get,
Hence, the final velocity is -6.11 m/s.
The result shows that the car moves in the opposite direction. It is unreasonable that on the application of brakes, the car will move in the opposite direction.
The unreasonable premise is that the car traveling at a speed of 13.89 m/s can decelerate at a rate of 0.4 m/s2 in 50 seconds.
An elevator filled with passengers has a mass of 1700 kg.
(a) The elevator accelerates upward from rest at a rate of 1.20 m/s2 for 1.50 s. Calculate the tension in the cable supporting the elevator.
(b) The elevator continues upward at constant velocity for 8.50 s. What is the tension in the cable during this time?
(c) The elevator decelerates at a rate of 0.600 m/s2 for 3.00 s. What is the tension in the cable during deceleration?
(d) How high has the elevator moved above its original starting point, and what is its final velocity?
(a) Give an example of different net external forces acting on the same system to produce different accelerations. (b) Give an example of the same net external force acting on systems of different masses, producing different accelerations. (c) What law accurately describes both effects? State it in words and as an equation.
Consider the tension in an elevator cable during the time the elevator starts from rest and accelerates its load upward to some cruising velocity. Taking the elevator and its load to be the system of interest, draw a free-body diagram. Then calculate the tension in the cable. Among the things to consider are the mass of the elevator and its load, the final velocity, and the time taken to reach that velocity.
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