# How do you find displacement on a graph in calculus?

Table of Contents

## How do you find displacement on a graph in calculus?

The displacement can be found by calculating the total area of the shaded sections between the line and the time axis. There is a triangle and a rectangle – the area of both must be calculated and added together to give the total displacement.

**What does a displacement time graph show?**

Displacement-time graphs show how the displacement of a moving object changes with time. A sloping line on a displacement-time graph shows that the object is moving. In a displacement-time graph, the slope or gradient of the line, is equal to the velocity of the object.

**What is the formula to find displacement?**

Displacement (s) of an object equals, velocity (u) times time (t), plus ½ times acceleration (a) times time squared (t2).

### What does the area under the distance time graph represent?

The area under distance time graph gives nothing. Therefore, the area under the curve of the velocity time graph gives distance covered by the body. Note: The gradient of the curve in the distance time graph defines the velocity of the body.

**What does the slope of displacement time graph gives?**

In a displacement – time graph, slope gives velocity.

**What is the slope of the distance time graph?**

speed

In a distance-time graph, the slope or gradient of the line is equal to the speed of the object.

## Why is displacement the area under curve?

You can’t fully represent displacement by finding the area, since as a vector quantity, displacement also requires a direction. Finding the area only gives an amount, no direction. The area under the curve is the magnitude of the displacement, which is equal to the distance traveled (only for constant acceleration).

**What is the slope of a distance time graph called?**

The slope of a distance-time graph indicates the rate of change of distance and it is termed as speed.

**What does displacement mean in calculus?**

The displacement is simply the difference in the position of the two marks and is independent of the path taken when traveling between the two marks. The distance traveled, however, is the total length of the path taken between the two marks.

### How do you find distance when given velocity and time calculus?

In particular, when velocity is positive on an interval, we can find the total distance traveled by finding the area under the velocity curve and above the t -axis on the given time interval.