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

Question

★ Show the movement of the body graphically
★ 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 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.