Solved Given the following position vs time graphs, sketch | Chegg.com - Free Printable

To solve this problem, we need to understand the relationship between position, velocity, and acceleration graphs. Here are the key rules:

1. Position vs. Time ($x$-$t$) Graph:
* The slope of the line represents velocity.
* A flat horizontal line means zero velocity (object is stopped).
* A straight diagonal line means constant velocity.
* A curved line means changing velocity (acceleration). If it curves up like a smile $\cup$, acceleration is positive. If it curves down like a frown $\cap$, acceleration is negative.

2. Velocity vs. Time ($v$-$t$) Graph:
* The value on the y-axis tells you the speed and direction.
* The slope of the line represents acceleration.
* A flat horizontal line means zero acceleration (constant velocity).
* A straight diagonal line means constant acceleration.

3. Acceleration vs. Time ($a$-$t$) Graph:
* This graph shows how the slope of the velocity graph changes.
* Zero acceleration is a flat line on the t-axis.
* Positive acceleration is a flat line above the axis.
* Negative acceleration is a flat line below the axis.

Let's go through each graph one by one.

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Graph 1

* Position: Horizontal flat line. The object is not moving. Position stays the same.
* Velocity: Since position isn't changing, velocity is zero. Draw a flat line on the time axis ($y=0$).
* Acceleration: Since velocity is constant at zero, acceleration is zero. Draw a flat line on the time axis ($y=0$).

Graph 2

* Position: Straight diagonal line going up. Constant positive slope.
* Velocity: The slope is constant and positive. So, velocity is a positive constant value. Draw a flat horizontal line above the time axis.
* Acceleration: Since velocity is constant (flat line), the slope of the velocity graph is zero. Acceleration is zero. Draw a flat line on the time axis ($y=0$).

Graph 3

* Position: Straight diagonal line going down. Constant negative slope.
* Velocity: The slope is constant and negative. So, velocity is a negative constant value. Draw a flat horizontal line below the time axis.
* Acceleration: Velocity is constant, so acceleration is zero. Draw a flat line on the time axis ($y=0$).

Graph 4

* Position: Curve getting steeper (concave up). Slope starts near zero and increases.
* Velocity: Since the slope is increasing, velocity is increasing from zero. It’s a straight diagonal line going up starting from the origin.
* Acceleration: The velocity graph is a straight line with a positive slope. This means acceleration is positive and constant. Draw a flat horizontal line above the time axis.

Graph 5

* Position: Curve getting steeper downwards (concave down). Slope starts near zero and becomes more negative.
* Velocity: The slope is becoming more negative. Velocity starts at zero and goes down linearly. Draw a straight diagonal line going down from the origin into the negative region.
* Acceleration: The velocity graph is a straight line with a negative slope. This means acceleration is negative and constant. Draw a flat horizontal line below the time axis.

Graph 6

* Position: Curve flattening out (concave down). Slope starts steep positive and decreases to zero.
* Velocity: Velocity starts high positive and decreases linearly to zero. Draw a straight diagonal line starting high on the y-axis and going down to cross the time axis at the end.
* Acceleration: The velocity graph has a constant negative slope. Acceleration is negative and constant. Draw a flat horizontal line below the time axis.

Graph 7

* Position: Curve flattening out in the positive region (concave up). Slope starts steep negative and approaches zero.
* Velocity: Velocity starts large negative and increases linearly toward zero. Draw a straight diagonal line starting low in the negative region and going up to approach the time axis.
* Acceleration: The velocity graph has a constant positive slope (it's going up). Acceleration is positive and constant. Draw a flat horizontal line above the time axis.

Graph 8

* Position: Parabola opening downward (like an upside-down U). Slope starts positive, goes to zero at the top, then becomes negative.
* Velocity: Velocity starts positive, decreases linearly through zero, and becomes negative. Draw a straight diagonal line starting in the positive region, crossing the time axis in the middle, and ending in the negative region.
* Acceleration: The velocity graph has a constant negative slope. Acceleration is negative and constant. Draw a flat horizontal line below the time axis.

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Final Answer:

Here is the description of what to draw for each empty graph box:

Row 1 (Graphs 1–4):
* 1 Velocity: Flat line on the x-axis (zero).
* 1 Acceleration: Flat line on the x-axis (zero).
* 2 Velocity: Flat horizontal line above the x-axis (positive constant).
* 2 Acceleration: Flat line on the x-axis (zero).
* 3 Velocity: Flat horizontal line below the x-axis (negative constant).
* 3 Acceleration: Flat line on the x-axis (zero).
* 4 Velocity: Straight diagonal line starting at origin and going up-right (positive slope).
* 4 Acceleration: Flat horizontal line above the x-axis (positive constant).

Row 2 (Graphs 5–8):
* 5 Velocity: Straight diagonal line starting at origin and going down-right (negative slope).
* 5 Acceleration: Flat horizontal line below the x-axis (negative constant).
* 6 Velocity: Straight diagonal line starting high on y-axis and going down to cross x-axis at the end.
* 6 Acceleration: Flat horizontal line below the x-axis (negative constant).
* 7 Velocity: Straight diagonal line starting low on negative y-axis and going up to approach x-axis.
* 7 Acceleration: Flat horizontal line above the x-axis (positive constant).
* 8 Velocity: Straight diagonal line starting positive, crossing zero in the middle, ending negative.
* 8 Acceleration: Flat horizontal line below the x-axis (negative constant).