Calculate the total distance covered by the particle shown in the speed-time graph.

Question

ScanSolve AI Tutor · Accepted Answer

The question asks to calculate a quantity based on the provided speed-time graph. Assuming the question asks for the total distance covered by the particle, we will calculate the area under the graph. The motion can be divided into three segments:

Segment 1 (0 to 10 s): Deceleration from $35 \text{ m/s}$ to $20 \text{ m/s}$ . This is a trapezium.
Segment 2 (10 to 25 s): Constant speed of $20 \text{ m/s}$ . This is a rectangle.
Segment 3 (25 to 40 s): Deceleration from $20 \text{ m/s}$ to $0 \text{ m/s}$ (rest). This is a triangle.

Calculate the distance covered in the first segment (0 to 10 s).
The area of a trapezium is given by $\frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$ .
$S_1 = \frac{1}{2} (35 \text{ m/s} + 20 \text{ m/s}) \times 10 \text{ s}$ $S_1 = \frac{1}{2} (55 \text{ m/s}) \times 10 \text{ s}$ $S_1 = 55 \text{ m/s} \times 5 \text{ s} = 275 \text{ m}$
Calculate the distance covered in the second segment (10 to 25 s).
The area of a rectangle is given by $\text{length} \times \text{width}$ .
$S_2 = 20 \text{ m/s} \times (25 \text{ s} - 10 \text{ s})$ $S_2 = 20 \text{ m/s} \times 15 \text{ s} = 300 \text{ m}$
Calculate the distance covered in the third segment (25 to 40 s).
The area of a triangle is given by $\frac{1}{2} \times \text{base} \times \text{height}$ .
$S_3 = \frac{1}{2} \times (40 \text{ s} - 25 \text{ s}) \times 20 \text{ m/s}$ $S_3 = \frac{1}{2} \times 15 \text{ s} \times 20 \text{ m/s}$ $S_3 = 15 \text{ s} \times 10 \text{ m/s} = 150 \text{ m}$
Calculate the total distance covered.
The total distance is the sum of the distances from each segment.
$S_{\text{total}} = S_1 + S_2 + S_3$ $S_{\text{total}} = 275 \text{ m} + 300 \text{ m} + 150 \text{ m}$ $S_{\text{total}} = 725 \text{ m}$
The total distance covered by the particle is $\text{725 m}$ .

Calculate the total distance covered by the particle shown in the speed-time graph.

Answer

Step-by-step solution

Calculate the distance covered in the first segment (0 to 10 s).

Calculate the distance covered in the second segment (10 to 25 s).

Calculate the distance covered in the third segment (25 to 40 s).

Calculate the total distance covered.

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