Question

What is the displacement of an object that starts at the origin and moves to position -8 m?

On a velocity vs time graph, what does a line of constant acceleration look like?

Answer 1

The displacement is a vector that is calculated by subtracting the final and initial positions of an object that has made a movement.

We know that initially the object was at the origin and moved to the -8m position.

Suppose that the movement was made on the x-axis. So:

d = [-8 - (0)]x

d = -8x

Regarding the second question.

When the acceleration is constant then the speed changes at a constant rate. Therefore the graph of velocity vs. time will look like a line with a negative slope (if the acceleration is negative) or a line with a positive slope (if the acceleration is positive)

For example. Suppose that the acceleration of gravity is 10 $m/s^2$

Now suppose you drop an object from a building.

At the initial moment (second 0) the speed is 0 m/s.

After 1 second the speed of the object will be 10 m/s.

After 2 seconds the speed of the object will be 20 m/s.

After 4 seconds the speed will be 40 m/s.

The graph of this example is shown in the attached figure. Note that it is a straight line.

Answer 2

#1

Displacement of object is defined as change in position

So here we have

$x_i = 0 m$

$x_f = -8 m$

so here displacement will be

$d = x_f - x_i$

$d = -8 - 0 = -8 m$

so displacement will be -8 m

#2

since acceleration is constant so we know that slope of velocity time graph will show acceleration

So here we know that acceleration is constant then the slope of velocity time graph must be constant

So it would be a straight line with constant slope