An automobile increased its speed uniformly from 20 m/s to 30 m/s at rate 5 m/s2. During this time it traveled 50 meters. How long did it take the automobile to make this change?
Answer(s): B
The answer can be determined because the rate of acceleration is uniform. Since the acceleration is 5 m/s2, the velocity increases by 5 m/s every second. If it starts at 20 m/s, after 1 second it will be going 25 m/s. After another second it will be going 30 m/s, so the total time is 2 seconds. You can also calculate this time by using the average speed. Since the object undergoes uniform acceleration, the average speed is 25 m/s. Using the distance traveled, the same result is obtained.t = d / v = 50 meters / 25 m/s = 2 seconds.
Which of the following demonstrations best illustrates Newton’s first law?
Answer(s): A
Newton’s first law (inertia) says an object in motion stays in motion, and an object at rest stays at rest, unless external forces act on them. Answer [Giving a billiard ball at rest on…] is an excellent demonstration because it shows the ball at rest and in motion. At rest, the ball stays at rest until a force acts on it. When the ball is moving, there is no force acting on the ball in the direction of motion. Thus, the natural state of the ball is to be at rest or moving with a constant speed. Answer [Trying without success to…] is not a good demonstration because the force of friction is what makes it hard to move the heavy object. Answer [Dragging a box in a table at…] is a good demonstration of equilibrium and friction. Answer “running a current through wires” has nothing to do with Newton’s first law.
A bowling ball with a mass of 4 kilograms moving at a speed of 10 meters per second hits a stationary 1 kg bowling ball in a head-on elastic collision. What is the speed of the stationary ball after the collision?
Answer(s): D
Since this is a head-on elastic collision, you could use conservation of kinetic energy and momentum to actually solve this problem. However, in this case, you only need to think through the answers to arrive at a correct conclusion. Clearly the ball after it’s struck won't be going 0 m/s. And since this is an elastic collision, and it is hit by a much larger ball, it must be going faster than the larger ball was originally moving. Therefore, the ballwill be moving at more than 10 m/s. If this were an inelastic collision where the balls stuck together, the ball would final velocity would be less than 10 m/s.
Which statement best explains why the work done by a gravitational force on an object does not depend on the path the object takes?
Answer(s): C
To determine how much work is done by a gravitational force, you should calculate the change in that object’s potential energy = mgh, where m = mass, g = the gravitational acceleration 9.8 m/s2 and h = height. Therefore, the work done only depends on the change in height and not on the path taken. In Answer [Work depends on the path when…], the work done by gravity doesn’t have anything to do with friction, so this is not a good explanation. Friction is a separate force. Answer [When an object falls down…], although true, doesn’t explain why the work doesn’t depend on the path.
A motorcycle weighs twice as much as bicycle and is moving twice as fast. Which of the following statements is true?
Kinetic energy is the energy of motion and is defined as 1/2mv2. Using this equation, if you double the mass and the velocity of an object, you find KE = 1/2(2mʹ)(2vʹ)2 or 8 times the original KE. Therefore, the motorcycle has 8 times as much kinetic energy as the bicycle.
Which of the following statements about electricity flowing through a circuit can be correctly derived from Ohm’s law?
Ohm’s law is that V = IR. Answer [Increasing the current increases the…] is the only relation that holds true using this equation. If the resistance doesn’t change, increasing the current on the right side must cause the voltage to also increase on the left side.
The density of helium is much lower than that of air. How does the speed of sound traveling through helium has compare to the speed of sound in air?
Sound travels much faster through helium than through air. Generally, the speed of sound can be calculated by speed = √(k × P / ρ), where k is the index of specific heats, P is pressure and ρ is density. Since helium has a much lower density, it would have a higher speed.
A liquid is held at its freezing point and slowly allowed to solidify. Which of the following statements about this event are true?
Freezing is an exothermic event; therefore, heat must be given off. The temperature of the material remains unchanged at the freezing point during the process.
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