Question

part 2 - graphing - distance vs time & speed vs time

1. the slope on a distance vs. time graph tells you an object’s (velocity, acceleration), and the slope on a velocity vs. time graph tells you the (velocity, acceleration) of the object. circle one answer in each pair of parentheses!
2. match the description with the distance vs. time graph.

a. slower, constant speed
b. no movement
c. faster, constant speed
d. deceleration
e. constant speed returning to starting position
f. acceleration

1. match the description with the speed vs. time graph.

a. at rest
b. constant speed
c. slower acceleration
d. deceleration
e. faster acceleration

Explanation:

Step1: Recall slope - meaning in distance - time graph

The slope of a distance - time graph is given by $\frac{\Delta d}{\Delta t}$, which is velocity. The slope of a velocity - time graph is given by $\frac{\Delta v}{\Delta t}$, which is acceleration. So for question 9, the answers are velocity and acceleration respectively.

Step2: Analyze distance - time graph for question 10

• Horizontal lines in a distance - time graph mean no movement (B) as $\frac{\Delta d}{\Delta t}=0$.
• Steeper non - horizontal straight lines mean faster constant speed (C), less steep non - horizontal straight lines mean slower constant speed (A). A line sloping downwards towards the starting position with constant slope means constant speed returning to starting position (E). Curved upwards lines mean acceleration (F) and curved downwards lines mean deceleration (D).

Step3: Analyze speed - time graph for question 11

• A horizontal line at speed = 0 means at rest (A). A non - zero horizontal line means constant speed (B). A less steep upward - sloping line means slower acceleration (C), a steeper upward - sloping line means faster acceleration (E), and a downward - sloping line means deceleration (D).

Answer:

1. velocity, acceleration

10.

• Horizontal line: B. No movement
• Less steep non - horizontal straight line: A. Slower, constant speed
• Steeper non - horizontal straight line: C. Faster, constant speed
• Curved downwards line: D. Deceleration
• Line sloping downwards towards starting position with constant slope: E. Constant speed returning to starting position
• Curved upwards line: F. Acceleration

11.

• Horizontal line at speed = 0: A. At rest
• Non - zero horizontal line: B. Constant speed
• Less steep upward - sloping line: C. Slower acceleration
• Downward - sloping line: D. Deceleration
• Steeper upward - sloping line: E. Faster acceleration