What is the time interval corresponding to an area of 20 meters under the velocity versus time graph of a car starting from rest?
To find the time interval corresponding to an area under the velocity versus time graph, we need to understand that the area under the graph represents the displacement of the object. In this case, we want to find the time interval corresponding to an area of 20 meters.
We can approach this problem by breaking down the graph into different shapes (rectangles and triangles) and calculating the area of each shape.
Assuming that the car starts from rest, the velocity versus time graph would begin at zero velocity. Let's say the graph shows a constant positive velocity for a certain time interval (rectangular shape), followed by a period where the velocity decreases uniformly (triangular shape).
1. Calculate the rectangular area:
- Determine the base of the rectangle, which represents the time interval.
- Determine the height of the rectangle, which represents the constant velocity. However, since the car starts from rest, the initial velocity is zero, so the height is also zero.
- Calculate the area of the rectangle using the formula: area = base × height.
2. Calculate the triangular area:
- Determine the base of the triangle, which represents the time interval.
- Determine the height of the triangle, which represents the change in velocity.
- Calculate the area of the triangle using the formula: area = 0.5 × base × height.
Add the areas of the rectangle and triangle to find the total area, which represents the displacement of the car.
Once we know the total area is 20 meters, we can set up the equation:
total area = area of rectangle + area of triangle
20 = (base of rectangle) * 0 + 0.5 * (base of triangle) * (height of triangle)
Simplifying the equation, we get:
20 = 0.5 * (base of triangle) * (height of triangle)
Now, we have one equation with two variables (base of the triangle and height of the triangle). To solve for the time interval, we need another piece of information. This could be the shape of the triangular area or any additional details about the velocity versus time graph.
Please provide more information about the shape of the graph or any other relevant details, so we can proceed with calculating the time interval.