The velocity(v)–displacement(x) graph of a particle moving in a straight line is shown below. (1) what is the relation between v and x ? (2) obtain the relation between acceleration and displacement and plot it.?

Question

Answer

Relation between v and x:
• The slope of the velocity-displacement graph gives the relationship between velocity and displacement.
• Since velocity is the rate of change of displacement, the slope represents the velocity at any point.

Relation between acceleration and displacement:
• Acceleration is the rate of change of velocity with respect to time.
• The acceleration can be determined by finding the slope of the velocity-displacement graph.
• By taking the derivative of the velocity function with respect to displacement, we can obtain the acceleration function.

Plotting the acceleration-displacement graph:
• To plot the acceleration-displacement graph, calculate the derivative of the velocity function.
• The derivative at each point represents the acceleration at that displacement.
• Plot these values on a new graph with displacement on the x-axis and acceleration on the y-axis.

Explanation:
• The acceleration graph will show how the acceleration of the particle changes with respect to displacement.
• Positive acceleration indicates the particle is speeding up, while negative acceleration means the particle is slowing down.
• The graph can help in understanding the behavior of the particle and its motion characteristics.

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