Question

The acceleration (a) - time (T) graph for the body starting from rest is given below. The maximum speed of the body is

• A. \(40\text{ }\mathrm{m}/\mathrm{s}\)
• B. \(80\text{ }\mathrm{m}/\mathrm{s}\)
• C. \(160\text{ }\mathrm{m}/\mathrm{s}\)
• D. \(200\text{ }\mathrm{m}/\mathrm{s}\)

Hint:

The area under an acceleration-time graph gives the change in speed.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Change in velocity equals the area under the acceleration-time graph.
The body starts from rest and acceleration stays positive, so speed rises until \(t = 10\) s.

Step 2: Area of the Triangle
The graph is a triangle with height \(8\ \text{m/s}^2\) and base \(10\) s.

Step 3: Calculation
\(v_{max} = \dfrac{1}{2}\times 10\times 8 = 40\ \text{m/s}\)

Final Answer:
The maximum speed reached is 40 m/s. \[ \boxed{\text{(A) }40\text{ m/s}} \]