Question

1. sketch a distance vs. time graph that shows constant speed.
2. sketch a distance vs. time graph that shows not moving.
3. sketch a distance vs. time graph that shows speed increasing.
4. sketch a distance vs. time graph that shows speed decreasing.

Explanation:

Step1: Constant speed graph

A constant - speed graph has a straight - line slope. The distance $d$ changes linearly with time $t$, and the equation is $d = vt$ (where $v$ is the constant speed). So, it is a straight line with a non - zero slope.

Step2: Not moving graph

When not moving, the distance does not change with time. So, the graph is a horizontal line where the distance value remains the same as time progresses.

Step3: Increasing speed graph

For increasing speed, the slope of the distance - time graph gets steeper as time goes on. This is because the rate of change of distance (speed) is increasing.

Step4: Decreasing speed graph

For decreasing speed, the slope of the distance - time graph gets less steep as time goes on. The rate of change of distance (speed) is decreasing.

Answer:

1. Draw a straight line with a non - zero slope for constant speed.
2. Draw a horizontal line for not moving.
3. Draw a curve where the slope gets steeper over time for increasing speed.
4. Draw a curve where the slope gets less steep over time for decreasing speed.