A person walks 4 meters in a single direction. He or she then changes directions and walks an additional 9 meters. What is the total magnitude of the displacement of the person?
Answer(s): C
Displacement is a vector that indicates the change in the location of an object. Answer 1 would be correct if the question asked for the total distance the person walked or if the person didn’t change direction. If the person turned around 180°, the displacement could be as small as 5 meters. If the person changed directions only a fraction of a degree, its magnitude would be less than 13 meters, not as large as 13 meters.
A lead sphere 10 centimeters in diameter is attached to a 10-meter wire and suspended from a beam in a large warehouse. A lead sphere 1 meter in diameter is hung next to the smaller sphere, almost touching. Ignoring friction, which statement is true?
Answer(s): D
There will be a gravitational force of attraction between the two spheres determined by the universal constant of gravity, the distance between the spheres, and the mass of the spheres. Since both objects are affected by this force (remember, Newton’s 3rd law says the force needs to be equal and opposite), both objects will experience a slight acceleration and start moving towards each other a tiny amount (when we ignore friction). Using F = ma, you know that the less massive sphere will experience a larger acceleration than the more massive one.
Two cars driving in opposite directions collide. If you ignore friction and any other outside interactions, which of the following statements is always true?
Answer(s): A
In a closed system (when you ignore outside interactions), the total momentum is constant and conserved. The total energy would also be conserved, although not the sum of the potential and kinetic energy. Some of the energy from the collision would be turned into thermal energy (heat) for example. Nor is the total velocity conserved, even though the velocity is a component of the momentum, since the momentum also depends on the mass of the cars. The impulse is a force over time that causes the momentum of a body to change. It doesn’t make sense to think of impulse as conserved, since it’s not necessarily constant throughout a collision.
Which statement correctly describes the elastic limit of a metal rod?
When an external force deforms a solid material, it will return to its initial position when the force is removed. This is called elasticity and is exhibited by springs. If too much force is applied and the elastic limit is exceeded, the rod won’t return to its original shape any longer. As with springs, the deformation is directly proportional to the stress. The elastic limit occurs in rods subjected to a tensile force when the strain stops being directlyproportional to the stress. The typical pattern when the force increases is that the strain increases linearly, then it doesn’t increase as much, and then it breaks.
A square has a perimeter of x and an area of 2x. What is x?
Answer(s): E
If a square has a perimeter of 32 (x), then its sides must be 8. The area is then: 8 × 8 = 64, or 2x.
A 1-gallon bottle containing 20% apple juice is mixed with a 2-gallon bottle containing 30% apple juice. What is the percentage of apple juice in the 3-gallon mixture?
Answer(s): B
This question can be solved in numerous ways. If 1 gallon has 20% apple juice, it means apple juice consists of 0.2 gallons. If the 2 gallon has 30% apple juice, it means apple juice consists of 0.6 gallons. Thus, there are a total of 0.8 gallons of apple juice in the mixture of the total 3 gallons.Find the percentage: (0.8 gallons of apple juice / 3 total gallons) × 100 = ~27%
This figure represents the score range for 520 students who took the OAT. How many students scored 360 or more points?
If 10% of test takers got a 360+ score, then find 10% of 520. 0.10 × 520 = 52
If (3a + a) − (2b − 3) = 7, find the values for 'a' and 'b'.
The easiest way to solve these is NOT to perform step by step algebra solutions that practice test makers put intheir solutions manual, but to simply (and quickly) plugin the answer choices and see if it works! Especially for a short, simple algebra problem like this one. In this scenario, both answer choices C & D work.
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