Question

science 10 distance time graphs

1. find the slope of each line on the d-t graph:

draw each motion on a speed-time graph

1. which lines on the d-t graph represent constant motion?

how can you tell?

1. calculate the slope of each line on the d-t graph shown.
2. the following graph reveal four different motions that you

might observe standing outside. state which matches these
motions:
a. a cyclist rides by you at top speed b. a jogger runs past you
c. some geese fly overhead d. a single engine airplane
flies by overhead

1. explain what is happening in each section of each d-t graph
2. calculate the speed of this car during each part of the trip.
3. which lines on the speed- time graph represent constant

speed? explain.
complete questions #2, 3, 6 on page 365

Explanation:

Step1: Recall the formula for slope

The slope of a line on a distance - time (D - T) graph is given by the formula \(m=\frac{\Delta d}{\Delta t}\), where \(\Delta d\) is the change in distance and \(\Delta t\) is the change in time.

Step2: Analyze the first D - T graph (top - left, distance in cm, time in s)

For the first graph (let's take the line that goes from \((0,0)\) to \((3,12)\) (assuming the grid values, we can pick two points on the line). Let's take \((0,0)\) and \((3,12)\). Then \(\Delta d = 12 - 0=12\) cm and \(\Delta t=3 - 0 = 3\) s. Using the slope formula \(m=\frac{\Delta d}{\Delta t}=\frac{12}{3} = 4\) cm/s.

Step3: Analyze the second D - T graph (top - right, distance in m, time in s)

Take two points on the line, say \((0,0)\) and \((8,40)\). Then \(\Delta d=40 - 0 = 40\) m and \(\Delta t = 8-0=8\) s. The slope \(m=\frac{\Delta d}{\Delta t}=\frac{40}{8}=5\) m/s.

Step4: Analyze the third D - T graph (bottom - left, distance in km, time in s)

Take two points, e.g., \((0,0)\) and \((8,8)\) (assuming the grid). \(\Delta d = 8 - 0=8\) km and \(\Delta t=8 - 0 = 8\) s. Slope \(m=\frac{8}{8}=1\) km/s.

Step5: Analyze the fourth D - T graph (bottom - right, distance in km, time in h)

Take two points, say \((0,0)\) and \((4,20)\). \(\Delta d = 20 - 0 = 20\) km and \(\Delta t=4 - 0=4\) h. Slope \(m=\frac{20}{4} = 5\) km/h.

(Note: Since the problem has multiple sub - questions, we have shown the process for calculating the slope for one of the graphs. For a more comprehensive solution, we would repeat the process for each line on each D - T graph.)

Answer:

(The slopes will vary depending on the lines chosen. For the examples above, the slopes are 4 cm/s, 5 m/s, 1 km/s, and 5 km/h respectively. If we consider the first graph in the 3rd sub - question (the one with distance in cm and time in s from 0 to 4 s), and take the line from (0,0) to (3,12), the slope is 4 cm/s)