A body starts from rest at position O and accelerates uniformly to position A then continues moving at a constant velocity for some time to position B before coming to rest at C

Question

Show the movement of the body graphically
Indicate:
The uniform acceleration of the body
It's retardation
The total distance covered by it
It's average speed

Answer 1

To show the movement of the body graphically, we can use a velocity-time graph.

On the graph, the x-axis represents time (t) and the y-axis represents velocity (v).

1. From position O to A: Since the body starts from rest, the initial velocity (at position O) is zero. As the body accelerates uniformly, the velocity increases linearly with time. Therefore, the line on the graph will be a straight line with a positive slope, representing uniform acceleration.

2. From A to B: The body continues to move at a constant velocity, which means the line on the graph will be a horizontal line, indicating zero acceleration.

3. From B to C: The body comes to rest at position C, which means the final velocity (at position C) is zero. As the body decelerates uniformly, the velocity decreases linearly with time. Therefore, the line on the graph will be a straight line with a negative slope, representing uniform deceleration.

To indicate the uniform acceleration and deceleration on the graph, we can draw arrows with labels "acceleration" and "deceleration" along the respective lines.

To determine the total distance covered by the body, we need to calculate the area under the velocity-time graph. The area under the line from O to A represents the distance covered during the acceleration phase. The area under the horizontal line from A to B represents the distance covered during the constant velocity phase. Finally, the area under the line from B to C represents the distance covered during the deceleration phase. Adding up these three areas will give us the total distance covered by the body.

To calculate the average speed, we divide the total distance by the total time taken.

Please keep in mind that without numerical values for time, acceleration, and distance, the graph can only represent the general shape and concept of the motion.