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
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
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.
To show the movement of the body graphically, we can plot a displacement-time graph.
Step 1: Uniform Acceleration from rest at position O to position A:
In this step, the body is accelerating uniformly from rest to position A.
- The graph will show a straight line starting from the origin O with a positive slope, indicating acceleration.
- The x-axis represents time, and the y-axis represents displacement.
- The uniform acceleration is represented by the slope of the line. Let's say it is denoted by "a".
Step 2: Constant Velocity from position A to position B:
In this step, the body continues moving at a constant velocity from position A to position B.
- The graph will show a straight line from position A to position B, parallel to the x-axis.
- The y-axis displacement remains constant during this time.
Step 3: Retardation from position B to position C:
In this step, the body slows down and comes to rest at position C.
- The graph will show a straight line with a negative slope, indicating retardation.
- The x-axis represents time, and the y-axis represents displacement.
- The retardation is represented by the slope of the line. Let's say it is denoted by "r".
Step 4: Total Distance covered by the body:
The total distance covered by the body is given by the sum of the distances traveled in each step.
- The distance covered during step 1 is given by the area under the acceleration line.
- The distance covered during step 2 is given by the width of the constant velocity line multiplied by the time spent at constant velocity.
- The distance covered during step 3 is given by the area under the retardation line.
- Summing up these distances will give the total distance covered.
Step 5: Average Speed:
The average speed of the body is given by the total distance covered divided by the total time taken.
- We can calculate the total time taken by adding the time taken during each step.
By following these steps and analyzing the graph, we can determine the uniform acceleration, retardation, total distance covered, and average speed of the body.