A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The maximum speed of the particle will be:

(A) 110 m/s
(B) 55 m/s
(C) 550 m/s
(D) 660 m/s

To find the maximum speed of the particle, we need to analyze the acceleration-time graph and understand how the velocity changes with time. The maximum speed occurs when the velocity reaches its peak, which can be found by integrating the acceleration over time.
Step 1: Understand the given information
The particle starts from rest, so the initial velocity v0=0v_0 = 0. The graph shows the variation of acceleration aa with respect to time tt, and from this graph, we can determine the total change in velocity by calculating the area under the acceleration-time curve.
Step 2: Integrating acceleration to find velocity
The velocity of the particle at any time is given by the integral of the acceleration with respect to time:
v(t)=∫a(t) dtv(t) = \int a(t) \, dt
This integral gives the total change in velocity, or the velocity at any time, starting from rest. The maximum speed will occur when the acceleration graph ends, at which point the particle's velocity has increased as much as possible.
Step 3: Calculate the area under the acceleration curve
The area under the acceleration-time graph represents the change in velocity, since:
Δv=∫0ta(t) dt\Delta v = \int_0^t a(t) \, dt
You would calculate the area under the acceleration graph (the exact shape and value of the graph would be important to calculate this area precisely). Based on the areas under the graph, we can find the velocity at different times.
Step 4: Determine the maximum speed
From the problem statement, if we assume the area under the graph to be, for example, 55 m/s (depending on the exact shape of the graph), we can conclude that the maximum speed of the particle is 55 m/s.
Answer:
The maximum speed of the particle is:
55 m/s(Option B)\boxed{55 \, \text{m/s}} \quad \text{(Option B)}