1-D, 2-D motion

Question 1

When v(x) = 4t^2, what does a(x) equal? What kind of graph is represented by a(x)? Does this graph show constant acceleration?

Answer 1

a(x) = 8t
linear
no, acceleration is not constant

Question 2

When is v(x) constant?

Answer 2

when the slope on a position vs. time graph is linear; velocity graph is a straight, horizontal line

Question 3

What is true when the net force on an object equals zero?

Answer 3

a = 0

velocity is constant

Question 4

What force(s) act on an object when it is in free-fall?

Answer 4

gravitational force (F(g))

Question 5

When considering projectile motion, what assumptions are made about the object’s acceleration in the x direction?

Answer 5

a(x) = 0

Question 6

If a football is kicked from the ground at a 37° angle with an initial velocity of 20 m/s, what is the total time of flight of the ball?

Answer 6

t = 1.22 s

[use y = y(0) + v(0)t – 1/2*gt^2]

Question 7

Describe the motion of an object moving uniformly in a circle.

Answer 7

acceleration is constant

direction of velocity is constantly changing, but magnitude is constant

Question 8

Describe the direction of position, velocity, tangential acceleration, centripetal acceleration, and centripetal force with respect to circular motion.

Answer 8

position vectors point in the negative radial direction (away from the origin)
velocity and tangential acceleration are always tangent to the circle
centripetal acceleration and centripetal force vectors point in the positive radial direction (toward the origin)

Question 9

Why are the magnitudes of the velocity and position vectors constant in circular motion?

Answer 9

|v| is constant because motion is uniform

|r| is constant because motion is circular

Question 10

Describe the relationship between mass, inertia, and weight.

Answer 10

mass indicates amount of matter as well as the amount of inertia
weight indicates gravitational force on a mass

Question 11

What are Newton’s first, second, and third laws?

Answer 11

1: an object in motion/at rest tends to stay in motion/at rest unless a net force acts upon it
2: F = ma
3: F(12) = -F(21)

Question 12

What accounts for differences in acceleration due to gravity?

Answer 12

mass –> larger mass experiences smaller acceleration

Question 13

Describe F(g) where a person stands on a scale in an elevator. What does the scale read if the elevator is stationary? Moving upward at a constant velocity? Accelerating upward? Accelerating downward? In free-fall?

Answer 13

Stationary: ∑F(y) = ma(y) where a(y) = 0, so N = mg
Moving upward w/ constant v: a(y) = 0, so N = mg
Accelerating upward: N = ma(y)+mg => heavier
Accelerating downward: N = ma(y)+mg => lighter
Free-fall: N = mg