A body starts from rest at position O and accelerates uniformly to a position A then continues moving at a constant velocity for some time to position B before coming to rest
★ Show the movement of the body graphically
★ It's retardation
★ The total distance covered by it
★ it's average speed
To show the movement of the body graphically, we can plot a position-time graph. Let's assume that time is represented on the x-axis, and position is represented on the y-axis.
The graph would look like this:
|
A |\
| \
| \
| \
| \
| \
| \
O |-------\
| \
| \
| \
| \
B |____________\
In this graph, the body starts from rest at position O, so the graph starts at the origin (0,0). Then, it accelerates uniformly to position A, represented by the increasing slope of the graph. After reaching position A, the body moves at a constant velocity, represented by the straight line portion of the graph from point A to point B. Finally, the body comes to rest at position B, represented by the flat line portion of the graph after point B.
The retardation of the body is represented by the flat line portion of the graph after point B. Since the body is coming to rest, the velocity is decreasing at a constant rate, resulting in negative acceleration or retardation.
To determine the total distance covered by the body, we need to calculate the area under the graph. In this case, the area is divided into two parts: the triangle formed by O, A, and the x-axis, and the rectangle formed by A, B, and the x-axis.
The total distance covered is given by:
Total distance = Area of triangle + Area of rectangle
To calculate the area of the triangle, we can use the formula:
Area of triangle = 0.5 * base * height
The base is the time taken to reach position A, and the height is the position at A.
To calculate the area of the rectangle, we can use the formula:
Area of rectangle = length * width
The length is the time taken to move from position A to position B, and the width is the position at A.
The average speed of the body can be calculated by dividing the total distance covered by the time taken.
To answer your questions step-by-step:
1. Showing the movement graphically:
To graphically represent the motion of the body, you can plot the distance from the starting point (O) on the y-axis and time on the x-axis. The graph will consist of three stages:
- Stage 1: From time t=0 to the time it reaches position A, the body's distance will increase with time due to uniform acceleration.
- Stage 2: Once the body reaches position A, it will continue moving at a constant velocity, represented by a horizontal line segment until it reaches position B.
- Stage 3: After reaching position B, the body comes to rest, which will be represented by a vertical line segment from position B to the time axis.
2. Determining the retardation:
Since the body starts from rest and comes to a stop at position B, the term "retardation" refers to the acceleration in the opposite direction of motion. Therefore, the retardation of the body will be zero during stages 1 and 2, as it accelerates and then moves at a constant velocity. However, during stage 3, it experiences negative acceleration (retardation) to come to rest.
3. Calculating the total distance covered:
To calculate the total distance covered, you need to consider the distances covered in the three stages. In stage 1, you can use the formula for uniformly accelerated motion, which is S = (u * t) + (0.5 * a * t^2), where S is the distance covered, u is the initial velocity (which is zero in this case), t is the time, and a is the acceleration. In stage 2, the distance is determined by the constant velocity, so you can multiply the velocity by the time it stays at that velocity. Finally, in stage 3, the distance covered is equal to the distance from position B to the starting point, which can be calculated as the negative of the distance covered in stage 1.
4. Finding the average speed:
To calculate the average speed, you can divide the total distance covered by the total time taken. Since the starting velocity is zero, the average speed will be equal to the average velocity.
Please note that specific values for time, acceleration, and distances are needed to provide precise numerical answers.