MCAT Physics and Math UPDATED
ACTUAL Questions and CORRECT
Answers
Metric system - CORRECT ANSWER- A system of measurements based on the powers of
ten; most commonly used in scientific disciplines
If the newton is the product of kilograms and meters/second^2, what units comprise the
pound? - CORRECT ANSWER- Force will obey the same relationship with mass and
acceleration, regardless of the unit system. Force is always the product of mass and
acceleration, so one pound (lb) must be equal to one slug*ft/s^2
Order the following units from smallest to largest: centimeters, angstrom, inch, mile, foot. -
CORRECT ANSWER- Angstrom < Centimeters < Inch < Foot < Mile
Vectors - CORRECT ANSWER- A mathematical quantity that has both magnitude and
direction.
Scalars - CORRECT ANSWER- A mathematical quantity that lacks directional
Resultant - CORRECT ANSWER- The sum, difference or product of vector mathematics;
also refers to the sum or difference of two waves
X = Vcos() and... - CORRECT ANSWER- Y = Vsin()
Find the x- and y-components of the following vector: V = 10 m/s, () = 30 degrees -
CORRECT ANSWER- X = Vcos = 10cos(30) = 10squareroot(3) / 2 = 5squareroot(3) m/s
Y = Vsin = 10 sin(3) = 10/2 = 5 m/s
What is the magnitude of the vector with the following components? X = 3 m/s, Y = 4 m/s -
CORRECT ANSWER- V = squareroot(3^2 + 4^2) = squareroot(25) = 5 m/s
,What are the magnitude and directions of the resultant vectors from the following cross
products: C = AxB and D = BxA?
A: X = -3 N, Y=0
B: X = 0, Y = +4 m - CORRECT ANSWER- The magnitude of the resultant vector is simply
the product of the magnitudes of the factor vectors and the sine of the angle between them. In
this case, because one is oriented in the x-direction and the other is in the y-direction, the
angle between them is 90.
|A| x |B| x sin90 = 3 N x 4 m x 1= 12 N*m
The magnitude is therefore 12 N*m.
Now, to determine the direction of C, start by pointing your right thumb towards the left
(negative x-direction). Your fingers will point toward the top of the page (positive y-
direction). Your palm is therefore pointing into the page.
Now, to determine the direction of D, start by pointing your right thumb towards the top of
the page (positive y-direction). Your fingers will point towards the left (negative x-direction).
Your palm is therefore pointing out of the page.
Therefore, C is 12 N*m [into the page] and D is 12 N*m [out of the page].
When calculating the sum of vectors A and B (A+B) we put the tail of B at the tip of A. What
would be the effect of reversing this order (B+A)? - CORRECT ANSWER- Vector addition,
unlike vector multiplication, is a commutative function. The resultant of A+B is the same as
B+A, so there would be no difference between the two resultant.
When calculating the difference of vectors A and B (A-B) we invert B and put the tail of this
new vector at the tip of A. What would be the effect of reversing this order (B-A)? -
CORRECT ANSWER- Vector subtraction, like vector multiplication, is not a commutative
function. The resultant of A-B is the same magnitude as B-A, but is oriented in the opposite
direction.
How is the scalar calculated from the product of two vectors? How is the vector calculated? -
CORRECT ANSWER- Scalar: By using the dot product A.B = |A||B|
,Vector: By using the cross product AxB = |A||B|sin()
True or False: If C = AxB, where A is directed towards the right of the page, and B is directed
towards the top of the page, then C is directed midway between A and B at a 45 angle -
CORRECT ANSWER- False. This would be true of an addition problem in which both
vectors have equal magnitude, but it is never true for vector multiplication. To find the
direction of C, we must use the right-hand rule. If the thumb points in the direction of A, and
the fingers point in the direction of B, then our palm, C, points out of the page.
Displacement - CORRECT ANSWER- The vector representing the straight-line distance and
direction from an initial point; not necessarily equal to total distance traveled, and measured
in meters.
What is the displacement of a man who walks 2 km east, then 2 km north, then 2 km west,
and then 2 km south? - CORRECT ANSWER- While his total distance traveled is 8 km, his
displacement is a vector quantity that represents the change in position. In this case, his
displacement is zero because the man ends up in the same place he started.
Velocity - CORRECT ANSWER- The rate of change in the displacement of an object;
measured in m/s
Speed - CORRECT ANSWER- The ratio of distance traveled to time; at any given point,
instantaneous speed is the magnitude of instantaneous velocity; measured in m/s
What is the relationship between instantaneous velocity and instantaneous speed? Between
average velocity and average speed? - CORRECT ANSWER- Instantaneous speed is the
magnitude of the instantaneous velocity vector. Average speed and average velocity may be
unrelated because speed does not depend on displacement, but rather the total distance
traveled divided by time.
True or False: Total distance traveled can never be less than the total displacement. -
CORRECT ANSWER- True. Displacement considers the most direct route between two
points. Distance will always be equal or larger in magnitude than displacement.
Provide a definition for displacement or velocity in terms of the other variable. - CORRECT
ANSWER- Velocity is the rate of the change in displacement of an object. Displacement is a
function of velocity acting over a period of time.
, Force - CORRECT ANSWER- A push or pull, measured in newtons (N)
Find the gravitation force between an electron and a proton that are 10^-11 m apart. (Note:
Mass of a proton = 1.67 x 10^-27 kg; mass of an electron = 9.11 x 10^-31 kg) - CORRECT
ANSWER- Use Newton's Law of Gravitation formula
Friction - CORRECT ANSWER- A non-conservative force that arises from the interactions
between two surfaces in contact
Normal force - CORRECT ANSWER- The force that two surfaces in contact exert on each
other that is perpendicular to the plane of contact
Mass - CORRECT ANSWER- A measure of inertia or of the amount of "stuff" in an object;
measured in kilograms
Weight - CORRECT ANSWER- The force of gravity acting on an object
Center of mass - CORRECT ANSWER- The point that acts as if the entire mass of an object
was concentrated at that point
Center of gravity - CORRECT ANSWER- A point such that the entire force of gravity acting
on an object can be thought of as acting at that point
Acceleration - CORRECT ANSWER- The rate of change in the velocity of an object; related
to force through mass and measure in m/s^2
When calculating frictional forces, how is direction assigned? - CORRECT ANSWER- The
direction of the frictional force always opposes movement. Once the instantaneous velocity
vector is known (or net force, in the case of static friction), the frictional force must be in the
opposite direction.
When no force is being applied, the velocity must be: - CORRECT ANSWER- If there is no
net force acting on an object, then the object is not experiencing an acceleration and has a
constant velocity.
