Question

name: handwritten
date:
hw 1.10
u1l10: free fall

1. circle all of the graphs below that represent accelerated motion. images of three graphs labeled 1, 2, 3

1. for any graphs you selected, explain why these graphs represent accelerated motion.

1. consider graph 2. describe a realistic situation that could correspond to the motion represented in that graph.

1. consider graph 3. describe a realistic situation that could correspond to the motion represented in that graph.

1. the graph to the right shows the velocity vs. time for an object in motion. list all intervals of time in which the object is accelerating. image of a velocity vs. time graph

Explanation:

Question 1: Circle all graphs representing accelerated motion

To determine accelerated motion, we analyze velocity - time or position - time graphs:

• Graph 1: Position - time graph. The slope (velocity) changes (decreases then increases), so acceleration (change in velocity) exists.
• Graph 2: Velocity - time graph. Velocity is constant (horizontal line), so acceleration is \(0\) (no acceleration).
• Graph 3: Velocity - time graph. Velocity increases (positive slope), so there is positive acceleration.

Thus, circle Graph 1 and Graph 3.

Question 2: Explain why selected graphs show accelerated motion

• Graph 1 (Position - Time): Acceleration occurs when velocity changes. The slope of a position - time graph is velocity. Here, the slope (velocity) first decreases (negative acceleration) then increases (positive acceleration), so velocity changes → accelerated motion.
• Graph 3 (Velocity - Time): The slope of a velocity - time graph is acceleration. A positive, non - zero slope means velocity increases at a constant rate → constant positive acceleration (accelerated motion).

Question 3: Realistic situation for Graph 2 (Constant Velocity)

Graph 2 has constant velocity (velocity - time graph is horizontal). A realistic situation: A car moving on a straight, flat highway with the cruise control set. The car’s speed (velocity) doesn’t change, so velocity is constant (acceleration \(= 0\)).

Question 4: Realistic situation for Graph 3 (Increasing Velocity)

Graph 3 shows velocity increasing over time (positive acceleration). A realistic situation: A car starting from rest at a stoplight and pressing the gas pedal steadily. The car’s speed (velocity) increases as it accelerates onto a highway.

Question 5: Intervals of Acceleration (Velocity - Time Graph)

Acceleration is the slope of the velocity - time graph. Positive slope = positive acceleration, negative slope = negative acceleration (still acceleration, as velocity changes).

• From \(t = 0\) to \(t = 5\) s: Velocity increases (positive slope) → accelerating.
• From \(t = 15\) to \(t = 25\) s: Velocity decreases (negative slope, but velocity is changing) → accelerating.

So the intervals are \(0 - 5\) seconds and \(15 - 25\) seconds.

Answer:

Question 1: Circle all graphs representing accelerated motion

To determine accelerated motion, we analyze velocity - time or position - time graphs:

• Graph 1: Position - time graph. The slope (velocity) changes (decreases then increases), so acceleration (change in velocity) exists.
• Graph 2: Velocity - time graph. Velocity is constant (horizontal line), so acceleration is \(0\) (no acceleration).
• Graph 3: Velocity - time graph. Velocity increases (positive slope), so there is positive acceleration.

Thus, circle Graph 1 and Graph 3.

Question 2: Explain why selected graphs show accelerated motion

• Graph 1 (Position - Time): Acceleration occurs when velocity changes. The slope of a position - time graph is velocity. Here, the slope (velocity) first decreases (negative acceleration) then increases (positive acceleration), so velocity changes → accelerated motion.
• Graph 3 (Velocity - Time): The slope of a velocity - time graph is acceleration. A positive, non - zero slope means velocity increases at a constant rate → constant positive acceleration (accelerated motion).

Question 3: Realistic situation for Graph 2 (Constant Velocity)

Graph 2 has constant velocity (velocity - time graph is horizontal). A realistic situation: A car moving on a straight, flat highway with the cruise control set. The car’s speed (velocity) doesn’t change, so velocity is constant (acceleration \(= 0\)).

Question 4: Realistic situation for Graph 3 (Increasing Velocity)

Graph 3 shows velocity increasing over time (positive acceleration). A realistic situation: A car starting from rest at a stoplight and pressing the gas pedal steadily. The car’s speed (velocity) increases as it accelerates onto a highway.

Question 5: Intervals of Acceleration (Velocity - Time Graph)

Acceleration is the slope of the velocity - time graph. Positive slope = positive acceleration, negative slope = negative acceleration (still acceleration, as velocity changes).

• From \(t = 0\) to \(t = 5\) s: Velocity increases (positive slope) → accelerating.
• From \(t = 15\) to \(t = 25\) s: Velocity decreases (negative slope, but velocity is changing) → accelerating.

So the intervals are \(0 - 5\) seconds and \(15 - 25\) seconds.