The area under a speed-time graph is the distance. This is because speed and distance are scalars. The area under a velocity-time graph is the displacement. Velocity can be negative if an object is moving backwards.

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

Important: The area between a velocity-time graph and the `time’ axis gives the displacement of the object. The slope is the same all the way from A to C, so the cyclist’s velocity is constant over the entire displacement he travels.

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).

The word displacement implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object.

(2). displacement=velocity × time =area of rectangle =Velocity-axis × time-axis, putting the value of velocity and time, then getting out the displacement.

Displacement can be negative because it defines a change in position of an object while carefully monitoring its direction. Then you walk back towards your original location in the −h opposite direction.

The answer is (a) as at the same time, the graph is showing two values of displacement which is not possible. Aakash EduTech Pvt.

If an object moves along a straight line, the distance travelled can be represented by a distance-time graph. In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.

(i) It tells us about the position of the body at any instance of time. (ii) From the graph, we can see the distance covered by the body during a particular interval of time. (iii) It also gives us information about the velocity of the body at any instance of time.

A distance-time graph shows how far an object has travelled in a given time. Distance is plotted on the Y-axis (left) and Time is plotted on the X-axis (bottom). A moving object is always ‘increasing’ its total length moved with time. ‘Curved lines’ on a distance time graph indicate that the speed is changing.

The slope of a distance-time graph represents speed. The steeper the slope is, the faster the speed. Average speed can be calculated from a distance-time graph as the change in distance divided by the corresponding change in time.

The principle is that the slope of the line on a position-time graph is equal to the velocity of the object. If the object is moving with a velocity of +4 m/s, then the slope of the line will be +4 m/s. If the object is moving with a velocity of -8 m/s, then the slope of the line will be -8 m/s.

In other words, the slope of the line tells us the rate of change of y relative to x. If the slope is 2, then y is changing twice as fast as x; if the slope is 1/2, then y is changing half as fast as x, and so on. In other words, if the line is near vertical then y is changing very fast relative to x.

When an object is moving with uniform velocity, the slope of graph is always a straight line. In other words slope of straight line of a distance-time graph shows that object is moving with uniform velocity. In the above graph, straight slope line shows that object is moving with uniform velocity.

The slope of a distance-time graph of a moving body gives its. Hint: Slope of a graph between two variables p on y-axis and q on x-axis is ΔpΔq.

A sloping line on a speed-time graph represents an acceleration . The sloping line shows that the speed of the object is changing. The object is either speeding up or slowing down. If the line slopes upward from left to right, this means the object is speeding up.

Graphical representation of motion: The most convenient way of studying the motion of a body is to construct a graph. In a graph: i) The magnitude of displacement, velocity or acceleration are plotted along the ordinates or the Y – axis ii) The time is plotted along the abscissa or the X – axis.

Displacement-time graph of a body moving with uniform velocity is always a straight line with slope =0.

If body moves with constant velocity then acceleration will be zero. So slope of v-t graph will be zero.

As far as I know, a position-time and displacement-time are exactly the same thing – though you could be using a slightly different definition. A displacement time graph simply shows where an object is at a given time.

Using the Slope Equation

1. Pick two points on the line and determine their coordinates.
2. Determine the difference in y-coordinates of these two points (rise).
3. Determine the difference in x-coordinates for these two points (run).
4. Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

The greater the velocity, the greater the gradient of the displacement–time graph. If the velocity is negative, then the gradient will also be negative (sloping downwards as time increases). If the velocity is zero then the gradient will also be zero (no slope at all).

Thus a graph of position versus time gives a general relationship among displacement, velocity, and time, as well as giving detailed numerical information about a specific situation.