Final answer:
A particle starts from rest, accelerates for 4 seconds, remains in uniform motion for next 4 seconds and then decelerates for 4 seconds. The acceleration-time graph can be divided into three parts: acceleration, uniform motion, and deceleration. The velocity-time graph can be drawn by integrating the acceleration values over time.
Step-by-step explanation:
The acceleration-time graph for the particle's motion can be divided into three parts: acceleration for the first 4 seconds, uniform motion for the next 4 seconds, and deceleration for the last 4 seconds. During the acceleration phase, the acceleration will be constant and positive. During the uniform motion phase, the acceleration will be zero. Lastly, during the deceleration phase, the acceleration will be constant and negative.
To draw the velocity-time graph, we can integrate the acceleration values over time. During the acceleration phase, the velocity will increase at a constant rate. During the uniform motion phase, the velocity will remain constant. Finally, during the deceleration phase, the velocity will decrease at a constant rate.
The acceleration-time graph will have three segments: positive acceleration, zero acceleration, and negative acceleration, each lasting for 4 seconds. The velocity-time graph will have a line sloping upwards for the first 4 seconds (constant acceleration), followed by a horizontal line for the next 4 seconds (constant velocity), and sloping downwards for the final 4 seconds (deceleration).
The question involves creating two graphs based on the description of a particle's motion: an acceleration-time graph and a velocity-time graph. The particle starts from rest, accelerates uniformly for 4 seconds, moves at a constant velocity for the next 4 seconds, then decelerates uniformly for another 4 seconds.
To plot the acceleration-time graph, draw a horizontal line above the time axis (positive acceleration) for the first 4 seconds, representing positive constant acceleration. Then, draw a horizontal line on the time axis (zero acceleration) for the next 4 seconds, representing no acceleration during uniform motion. Finally, draw a horizontal line below the time axis (negative acceleration) for the last 4 seconds, representing uniform deceleration.
The velocity-time graph would start at the origin since the particle starts from rest. For the first 4 seconds, the line would slope upwards, reflecting constant acceleration. Then, it would continue horizontally for 4 seconds, indicating constant velocity, and finally slope downwards for the last 4 seconds as the particle decelerates.