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(3) Suppose you travel at a speed of [tex]$2 \, \text{m/s}$[/tex] for 5 seconds, [tex]$3 \, \text{m/s}$[/tex] for 4 seconds, and [tex][tex]$5 \, \text{m/s}$[/tex][/tex] for 5 seconds.

a. Find the total distance covered.
b. Find the total time.

Sagot :

GinnyAnsweridn
Sure, let's solve this problem step-by-step.

### Step 1: Calculate the Distance for Each Segment

First, we need to determine the distance covered in each of the three time intervals with the given speeds.

Segment 1:
- Speed: [tex]\(2 \ \text{m/s}\)[/tex]
- Time: [tex]\(5 \ \text{seconds}\)[/tex]

[tex]\[ \text{Distance}_1 = \text{Speed}_1 \times \text{Time}_1 \][/tex]
[tex]\[ \text{Distance}_1 = 2 \ \text{m/s} \times 5 \ \text{seconds} = 10 \ \text{meters} \][/tex]

Segment 2:
- Speed: [tex]\(3 \ \text{m/s}\)[/tex]
- Time: [tex]\(4 \ \text{seconds}\)[/tex]

[tex]\[ \text{Distance}_2 = \text{Speed}_2 \times \text{Time}_2 \][/tex]
[tex]\[ \text{Distance}_2 = 3 \ \text{m/s} \times 4 \ \text{seconds} = 12 \ \text{meters} \][/tex]

Segment 3:
- Speed: [tex]\(1 \ \text{m/s}\)[/tex]
- Time: [tex]\(5 \ \text{seconds}\)[/tex]

[tex]\[ \text{Distance}_3 = \text{Speed}_3 \times \text{Time}_3 \][/tex]
[tex]\[ \text{Distance}_3 = 1 \ \text{m/s} \times 5 \ \text{seconds} = 5 \ \text{meters} \][/tex]

### Step 2: Calculate the Total Distance Covered

Now, let's add up the distances covered in each segment to find the total distance.

[tex]\[ \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 + \text{Distance}_3 \][/tex]
[tex]\[ \text{Total Distance} = 10 \ \text{meters} + 12 \ \text{meters} + 5 \ \text{meters} = 27 \ \text{meters} \][/tex]

### Step 3: Calculate the Total Time

Next, we need to find the total time by adding up all the time intervals.

[tex]\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 + \text{Time}_3 \][/tex]
[tex]\[ \text{Total Time} = 5 \ \text{seconds} + 4 \ \text{seconds} + 5 \ \text{seconds} = 14 \ \text{seconds} \][/tex]

### Summary:

- Distance covered in Segment 1: [tex]\(10 \ \text{meters}\)[/tex]
- Distance covered in Segment 2: [tex]\(12 \ \text{meters}\)[/tex]
- Distance covered in Segment 3: [tex]\(5 \ \text{meters}\)[/tex]
- Total Distance Covered: [tex]\(27 \ \text{meters}\)[/tex]
- Total Time: [tex]\(14 \ \text{seconds}\)[/tex]

So the total distance covered is [tex]\(27 \ \text{meters}\)[/tex] and the total time is [tex]\(14 \ \text{seconds}\)[/tex].
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