A speed-time graph shows an athlete accelerating from rest for 2 seconds to a speed of 8 m/s, then…

Question

A speed-time graph shows an athlete accelerating from rest for 2 seconds to a speed of 8 m/s, then maintaining that speed for 8 seconds. Calculate the total distance covered in the first 10 seconds.

ScanSolve AI Tutor · Accepted Answer

here's the solution for the speed-time graph problem:

a) Calculate the distance the athlete runs in the first 10 seconds.

The distance run is represented by the area under the speed-time graph. The graph can be divided into two parts: a triangle for the first 2 seconds and a rectangle for the next 8 seconds.

Calculate the distance for the first 2 seconds (area of the triangle).
The base of the triangle is 2 seconds and the height is 8 m/s.
$\text{Distance}_1 = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Distance}_1 = \frac{1}{2} \times 2\, \text{s} \times 8\, \text{m/s}$ $\text{Distance}_1 = 8\, \text{m}$
Calculate the distance from 2 seconds to 10 seconds (area of the rectangle).
The width of the rectangle is $10 - 2 = 8$ seconds and the height is 8 m/s.
$\text{Distance}_2 = \text{width} \times \text{height}$ $\text{Distance}_2 = 8\, \text{s} \times 8\, \text{m/s}$ $\text{Distance}_2 = 64\, \text{m}$
Calculate the total distance.
$\text{Total Distance} = \text{Distance}_1 + \text{Distance}_2$ $\text{Total Distance} = 8\, \text{m} + 64\, \text{m}$ $\text{Total Distance} = 72\, \text{m}$
The distance the athlete runs in the first 10 seconds is $\boxed{\textbf{72 m}}$ .

A speed-time graph shows an athlete accelerating from rest for 2 seconds to a speed of 8 m/s, then maintaining that speed for 8 seconds. Calculate the total distance covered in the first 10 seconds.

Answer

Step-by-step solution

Calculate the distance for the first 2 seconds (area of the triangle).

Calculate the distance from 2 seconds to 10 seconds (area of the rectangle).

Calculate the total distance.

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