Displacement, Velocity, and Acceleration
This is the rate of change of displacement as a function of time.
Velocity
This is the quantity of motion that you obtain when you take the derivative (tangent line) of a velocity vs. time graph at a single point. Be specific.
Instantaneous Acceleration
Frame of reference is a great tool for solving problems in physics; however, there is one known exception to the rules of relative motion and frames of reference. What is this exception?
The speed of light
In projectile motion, there is no acceleration in the horizontal (x) direction but there is this acceleration in the vertical (y) direction.
Gravity
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Minecwaft
A ball is thrown straight up from a point 2m above the ground. The ball reaches a maximum height of 3m above its starting point and then falls 5m to the ground. When the ball strikes the ground, what is its displacement from its starting point?
2m below
This is the quantity of motion you obtain when you take the integral (area under the curve) of a velocity vs. time graph.
Displacement
A student seated in a slowly moving bus holds a ball out at arm’s length and releases it. Immediately afterward, the driver of the bus applies the brakes, causing the bus to slow at a rate of 4 m/s2. Which of the following is closest to the vertical component of the acceleration of the ball while the bus slows down as seen by the student?
6, 10, 11, or 12 m/s2
10 m/s2
In two or three dimensional motion, mathematically, this is the reason that vectors in each of these dimensions do not affect each other.
They do no project onto one another e.g. their dot product is 0.
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Fortnite
An object in straight line motion has a displacement vs. time graph whose curvature is concave down. What does this denote about the acceleration of the object?
The acceleration is negative.
Refer to Google Doc Page 1
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Mr. Callahan decides one day to embrace his inner subway surfer and hop on top of a subway train. The subway train is moving down the track at a constant 80mph. Karma immediately strikes (because this is a really dumb idea) and upon reaching the top of the subway train, a bird traveling in the opposite direction at 15mph smacks Mr. Callahan right in the face. How fast, relative to Mr. Callahan, does the bird hit him in the face?
95mph
This is the angle at which a projectile should be launched to cover the maximum horizontal distance.
45 degrees
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The Legend of Zelda: Breath of the Wild
The speed v of an automobile moving on a straight road is given in meters per second as a function of time in t seconds by the following equation:
v(t) = 4 + 2t3
What is the acceleration of the automobile at t = 2s?
24 m/s2
Refer to Google Doc Page 2
+0.40 m/s
Car A is traveling east with a speed of 30 m/s. Car B is traveling north with speed of 40 m/s. What is the direction of the velocity of Car B relative to Car A?
53 degrees North of West
A small particle starts from rest from the origin of an xy-coordinate system and travels in the xy-plane. Its acceleration in the x-direction is 2.0 m/s2 , and its acceleration in the y-direction is 1.0 m/s2 . What is the x-coordinate of the particle when its y-coordinate is 12 m?
24m
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Super Mario Odyssey
An object of mass 10kg starts from rest at t = 0 and moves in a straight line. For time t > 0, the object's velocity v as a function of time t is given by:
v = 2t + 3t2,
where v is in m/s and t is in seconds. How far did the object travel during the first 10 s of its motion?
1100 m
The acceleration due to gravity on the Moon is gM. Suppose an astronaut on the Moon drops an object from a height of H. The time it would take the object to reach the Moon’s surface would be TM. The same object is dropped from the same height on Earth, where the acceleration due to gravity is gE. The time it takes the object to reach Earth’s surface is TE. Which of the following is a correct mathematical relationship for the two times?
TE = sqrt [(gE/gM)*TM]
Refer to Google Doc Page 3
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A projectile is launched with a speed of 30 m/s at an angle of 60 deg. above the horizontal. The projectile lands on a ledge that is 15m above the launch point, as shown. What are the horizontal and vertical components, vx and vy, of the velocity when the projectile lands?
vx = 15 m/s
vy = -19.5 m/s
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Stardew Valley