Question

The acceleration (\(a\)) -time (\(t\)) graph for the body starting from rest is as shown in the figure. The maximum speed of the body is

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

Hint:

The area under an acceleration-time graph gives the change in velocity. The speed is largest when the acceleration reaches zero.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The area under an acceleration-time graph equals the change in velocity. The body starts from rest, so the area equals its speed.

Step 2: Reading the graph
The acceleration falls straight from \(8\ \text{m/s}^{2}\) at \(t=0\) to zero at \(t=10\ \text{s}\). It stays positive, so the speed keeps rising until \(t=10\ \text{s}\).

Step 3: Calculation
The area is a triangle.
\(v_{max}=\dfrac{1}{2}\times10\times8=40\ \text{m/s}\)

Final Answer:
The maximum speed of the body is 40 m/s. \[ \boxed{\text{(D) }40\ \text{m/s}} \]