Question

1. below are four position vs. time graphs labeled (i) through (iv). identify which graph corresponds to each of the following situations and explain why you chose that graph. a. an object at rest. b. an object moving in the positive direction with a constant speed. c. an object moving in the negative direction with a constant speed. d. an object that is accelerating in the positive direction, starting from rest. 2. below are four velocity vs. time graphs labeled (i) through (iv). identify which graph corresponds to each of the following situations. explain why you chose that graph. a. an object at rest b. an object moving in the positive direction with a constant speed c. an object moving in the negative direction with a constant speed d. an object that is accelerating in the positive direction, starting from rest

Explanation:

1. Position - time graphs:

a. An object at rest has a constant position over time, so its position - time graph is a horizontal line. Graph (ii) is a horizontal line, so it represents an object at rest.

b. An object moving in the positive direction with a constant speed has a positive - slope straight - line on the position - time graph. Graph (iv) is a straight line with a positive slope, so it represents an object moving in the positive direction with a constant speed.

c. An object moving in the negative direction with a constant speed has a negative - slope straight - line on the position - time graph. Graph (i) is a straight line with a negative slope, so it represents an object moving in the negative direction with a constant speed.

d. An object that is accelerating in the positive direction starting from rest has a position - time graph that is a curve with an increasing slope. Graph (iii) is a curve with an increasing slope, so it represents an accelerating object in the positive direction starting from rest.

2. Velocity - time graphs:

a. An object at rest has a velocity of zero at all times. Graph (ii) has a velocity of zero (a horizontal line at \(v = 0\)), so it represents an object at rest.

b. An object moving in the positive direction with a constant speed has a positive constant velocity. Graph (iv) has a positive horizontal line, so it represents an object moving in the positive direction with a constant speed.

c. An object moving in the negative direction with a constant speed has a negative constant velocity. Graph (iii) has a negative horizontal line, so it represents an object moving in the negative direction with a constant speed.

d. An object that is accelerating in the positive direction starting from rest has a velocity - time graph that is a straight line with a positive slope starting from the origin (\(v=0\) at \(t = 0\)). Graph (i) is a straight line with a positive slope starting from the origin, so it represents an object accelerating in the positive direction starting from rest.

Answer:

1. Position - time graphs:

a. (ii)

b. (iv)

c. (i)

d. (iii)

2. Velocity - time graphs:

a. (ii)

b. (iv)

c. (iii)

d. (i)