journey to the bus stop
every morning tom walks along a straight road from his home to a bus stop, a distance of 160 meters.
the graph shows his journey on one particular day.
11. how far did tom walk in 50 seconds?
12. how long does it take tom to walk 100 meters?
13. what is toms speed for the first 50 seconds of his journey?
14. how far away is the bust stop from toms house?
15. what time interval was tom traveling the fastest? how do you know?
16. how long does it take tom to travel from 40 meters to 160 meters?
17. what distance does tom travel between 40 meters to 160 meters?
18. what is toms speed from 40 meters to 160 meters?
19. what time interval does tom walk back toward his house?
20. how long does tom wait at the bus stop?

Question

Accepted Answer

### Question 11
# Explanation:
## Step1: Analyze the graph
From the graph, we look at the time axis (x - axis) at 50 seconds and find the corresponding distance on the y - axis (distance from home).
## Step2: Read the value
At $t = 50$ seconds, the distance from home is 100 meters.
# Answer:
100 meters

### Question 12
# Explanation:
## Step1: Analyze the graph
We look for the distance of 100 meters on the y - axis (distance from home) and then find the corresponding time on the x - axis.
## Step2: Read the value
When the distance is 100 meters, the time is 50 seconds.
# Answer:
50 seconds

### Question 13
# Explanation:
## Step1: Recall the speed formula
The formula for speed $v=\frac{d}{t}$, where $d$ is the distance and $t$ is the time.
## Step2: Identify distance and time
For the first 50 seconds, the distance $d = 100$ meters and time $t=50$ seconds.
## Step3: Calculate speed
$v=\frac{100}{50}=2$ m/s.
# Answer:
2 m/s

### Question 14
# Explanation:
## Step1: Analyze the graph
The bus stop is the destination, so we look at the maximum value of the distance from home on the graph (when Tom reaches the bus stop and stops moving).
## Step2: Read the value
The distance from home to the bus stop is 160 meters.
# Answer:
160 meters

### Question 15
# Explanation:
## Step1: Recall the relationship between speed and slope
In a distance - time graph, the slope of the line represents the speed ($slope=\frac{\Delta d}{\Delta t}$, which is the same as speed). A steeper slope means a higher speed.
## Step2: Analyze the slopes of different intervals
- From 0 - 50 seconds: The slope is $\frac{100 - 0}{50-0}=2$ m/s.
- From 50 - 70 seconds: The slope is $\frac{40 - 100}{70 - 50}=\frac{- 60}{20}=- 3$ m/s (negative slope means moving back, speed magnitude 3 m/s).
- From 70 - 100 seconds: The slope is $\frac{160 - 40}{100 - 70}=\frac{120}{30} = 4$ m/s.
- From 100 - 120 seconds: The slope is 0 (stationary).

The steepest slope (highest speed) is in the interval 70 - 100 seconds because the slope of the line in this interval is the steepest (calculated speed is 4 m/s which is higher than other intervals).
# Answer:
The time interval is 70 - 100 seconds. We know this because the slope of the distance - time graph (which represents speed) is the steepest in this interval.

### Question 16
# Explanation:
## Step1: Find the time for 40 meters and 160 meters
- For 40 meters: From the graph, the time $t_1 = 20$ seconds (since at $t = 20$ s, $d = 40$ m).
- For 160 meters: The time $t_2=100$ seconds.
## Step2: Calculate the time interval
The time taken is $t_2 - t_1=100 - 20 = 80$ seconds.
# Answer:
80 seconds

### Question 17
# Explanation:
## Step1: Recall the distance formula for displacement (here, since we are calculating the distance traveled, we consider the path)
The distance traveled from 40 meters to 160 meters is $d=160 - 40+(100 - 40)$ (because Tom moves back from 100 to 40 meters and then forward to 160 meters). Wait, no, actually, in terms of the path:
- From 40 m (at $t = 20$ s) to 100 m (at $t = 50$ s): distance is $100 - 40 = 60$ m.
- From 100 m (at $t = 50$ s) to 40 m (at $t = 70$ s): distance is $100 - 40=60$ m.
- From 40 m (at $t = 70$ s) to 160 m (at $t = 100$ s): distance is $160 - 40 = 120$ m.

Total distance $d=60 + 60+120 = 240$ m? Wait, no, maybe the question is about the net displacement? No, the question says "distance traveled", so we need to consider the path. But if we consider the straight - line (displacement) from 40 m to 160 m, it is $160 - 40 = 120$ m. But from the graph:

Wait, at $t = 20$ s, $d = 40$ m; at $t = 100$ s, $d = 160$ m. But in between, Tom goes from 40 m to 100 m (50 s), then back to 40 m (70 s), then to 160 m (100 s).

So the distance traveled:
- From 40 m (20 s) to 100 m (50 s): $100 - 40=60$ m.
- From 100 m (50 s) to 40 m (70 s): $100 - 40 = 60$ m.
- From 40 m (70 s) to 160 m (100 s): $160 - 40=120$ m.

Total distance $=60 + 60+120=240$ m. But if the question is about the displacement (change in position), it is $160 - 40 = 120$ m. But the question says "distance does Tom travel", so we consider the path.

Wait, maybe I made a mistake. Let's re - examine the graph:

At $t = 20$ s, $d = 40$ m.

At $t = 50$ s, $d = 100$ m.

At $t = 70$ s, $d = 40$ m.

At $t = 100$ s, $d = 160$ m.

So the distance traveled from $d = 40$ m (t = 20 s) to $d = 160$ m (t = 100 s):

First, from 40 to 100: $100 - 40 = 60$ m.

Then, from 100 to 40: $100 - 40=60$ m.

Then, from 40 to 160: $160 - 40 = 120$ m.

Total distance $=60 + 60+120 = 240$ m.

But maybe the question is simpler, considering the final position minus initial position as distance (which is displacement, but sometimes in such problems, if the motion is along a straight line and we consider the path length, but maybe the question expects displacement). Wait, the problem says "distance does Tom travel", so it's the path length. But let's check the graph again.

Wait, maybe I misread the graph. Let's assume that from 40 m (at some time) to 160 m, the time between 40 m (say $t_1$) and 160 m ($t_2$):

If we take the initial time for 40 m as $t_1 = 20$ s and final time for 160 m as $t_2 = 100$ s.

The distance traveled:

From $t = 20$ to $t = 50$: distance from 40 to 100: 60 m.

From $t = 50$ to $t = 70$: distance from 100 to 40: 60 m.

From $t = 70$ to $t = 100$: distance from 40 to 160: 120 m.

Total: $60 + 60+120 = 240$ m. But maybe the question is wrong, or maybe I misinterpret. Alternatively, if we consider the net distance (displacement) from 40 m to 160 m, it is $160 - 40=120$ m. But the term "distance traveled" usually means path length. However, let's see the graph again. The vertical axis is distance from home. So when Tom is at 40 m, then goes to 100 m (moves 60 m away), then back to 40 m (moves 60 m back), then to 160 m (moves 120 m away). So total distance is $60 + 60+120 = 240$ m.

But maybe the question is intended to be displacement, so 120 m. But I think the correct way is to calculate the path length.

Wait, the problem says "What distance does Tom travel between 40 meters to 160 meters?". So we need to calculate the total length of the path he took from 40 m to 160 m.

So:

- From 40 m to 100 m: $100 - 40 = 60$ m.

- From 100 m to 40 m: $100 - 40 = 60$ m.

- From 40 m to 160 m: $160 - 40 = 120$ m.

Total distance $=60+60 + 120=240$ m.

But maybe the question has a typo, or maybe I misread the graph. Alternatively, if we consider the time when he is at 40 m is $t = 20$ s and at 160 m is $t = 100$ s, and in the graph, from $t = 20$ to $t = 100$, the distance traveled:

Wait, at $t = 20$, $d = 40$; $t = 50$, $d = 100$; $t = 70$, $d = 40$; $t = 100$, $d = 160$.

So the distance from $d = 40$ (t = 20) to $d = 160$ (t = 100) is:

$(100 - 40)+(100 - 40)+(160 - 40)=60 + 60+120 = 240$ m.

But maybe the answer is 120 m (displacement). But I think the correct answer is 120 m if we consider displacement, but distance traveled is 240 m. However, let's check the graph again. The vertical axis is distance from home. So when he is at 40 m, then goes to 100 m (distance from home increases by 60 m), then back to 40 m (distance from home decreases by 60 m), then to 160 m (distance from home increases by 120 m). So the total distance traveled (path length) is $60+60 + 120 = 240$ m.

But I am confused. Maybe the question is wrong, or maybe I misinterpret. Alternatively, maybe the time when he is at 40 m is $t = 20$ s and at 160 m is $t = 100$ s, and the distance between 40 m and 160 m is $160 - 40 = 120$ m (displacement). So I think the answer is 120 m (if we consider displacement) or 240 m (if we consider distance traveled). But let's see the graph again. The graph shows that from 40 m (at t = 20 s) to 160 m (at t = 100 s), the path is: up to 100 m, down to 40 m, up to 160 m. So the total distance is $60+60 + 120 = 240$ m.

But maybe the question is intended to be displacement, so 120 m. I think I will go with 120 m as the answer (maybe the question means displacement).

# Answer:
120 meters (or 240 meters depending on interpretation, but likely 120 meters as displacement)

### Question 18
# Explanation:
## Step1: Recall the speed formula
$v=\frac{d}{t}$, where $d$ is the distance traveled (path length) or displacement. Let's assume we use displacement (120 m) and time from $t = 20$ s to $t = 100$ s, so $t=100 - 20 = 80$ s.
## Step2: Calculate speed
$v=\frac{120}{80}=1.5$ m/s. But if we use distance traveled (240 m), $v=\frac{240}{80}=3$ m/s. But let's check the graph again.

Wait, from 40 m (t = 20 s) to 160 m (t = 100 s), the time taken is $100 - 20 = 80$ s. The displacement is $160 - 40 = 120$ m. The distance traveled is $240$ m. But speed is usually calculated as $\frac{\text{distance traveled}}{\text{time}}$ or $\frac{\text{displacement}}{\text{time}}$. In a distance - time graph, the speed (instantaneous or average) can be calculated as $\frac{\Delta d}{\Delta t}$ where $\Delta d$ is the change in distance from home (displacement). So if we consider the average speed from 40 m to 160 m (displacement), $v=\frac{160 - 40}{100 - 20}=\frac{120}{80}=1.5$ m/s. But if we consider the total distance traveled, $v=\frac{240}{80}=3$ m/s.

But let's see the intervals:

- From 20 - 50 s: speed is $\frac{100 - 40}{50 - 20}=\frac{60}{30}=2$ m/s.

- From 50 - 70 s: speed is $\frac{40 - 100}{70 - 50}=\frac{- 60}{20}=- 3$ m/s (magnitude 3 m/s).

- From 70 - 100 s: speed is $\frac{160 - 40}{100 - 70}=\frac{120}{30}=4$ m/s.

So the average speed from 40 m (t = 20 s) to 160 m (t = 100 s) is $\frac{\text{total distance traveled}}{\text{total time}}=\frac{60 + 60+120}{80}=\frac{240}{80}=3$ m/s.

So the answer is 3 m/s.

# Answer:
3 m/s

### Question 19
# Explanation:
## Step1: Recall the meaning of negative slope
In a distance - time graph, a negative slope means that the distance from home is decreasing, which means Tom is walking back toward his house.
## Step2: Analyze the graph
We look for the interval where the slope of the distance - time graph is negative (distance from home is decreasing). From 50 seconds to 70 seconds, the distance from home decreases from 100 meters to 40 meters, so the slope is negative.
# Answer:
50 - 70 seconds

### Question 20
# Explanation:
## Step1: Analyze the graph
Tom waits at the bus stop when the distance from home is constant (the graph is a horizontal line).
## Step2: Identify the time interval
From 100 seconds to 120 seconds, the distance from home remains 160 meters (

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QUESTION IMAGE

Question

Explanation:

Question 11

Step1: Analyze the graph

Step2: Read the value

Step1: Analyze the graph

Step2: Read the value

Step1: Recall the speed formula

Step2: Identify distance and time

Step3: Calculate speed

Answer:

Question 12