# Motion Graphs

## Motion Graphs Revision

**Motion Graphs**

When objects are in **motion**, their **distance** and** velocity** can be plotted against time. We can show how these quantities change over a period of time.

**Distance-time graphs**

**Distance-time** graphs show how an objects **distance** changes with time. Distance should be plotted on the y axis, and time on the x axis.

We know:

\text{speed} = \dfrac{\text{distance}}{\text{time}}

The gradient of the distance-time graph is:

\dfrac{\text{change in vertical axis}}{\text{change in horizontal axis}} = \dfrac{\text{distance}}{\text{time}}

Therefore the **gradient** of a distance-time graph is equal to the **speed**.

- The steeper the graph is, the higher the speed.
- If the graph is a straight line, then the
**speed is constant**. - If the graph is flat, then no distance is travelled in the time period, so the object is
**stationary**. - If the graph is curved upwards, then the object is
**accelerating**(speeding up). If the graph is a curve that is levelling out, then the object is**decelerating**(slowing down).

**Velocity-time graphs**

**Velocity-time** graphs show how an objects **velocity **changes over time. The gradient of a velocity-time graph is:

\dfrac{\text{change in vertical axis}}{\text{change in horizontal axis}} = \dfrac{\text{velocity}}{\text{time}}

Therefore the **gradient** of a velocity time graph is equal to the **acceleration**.

- Straight uphill sections represent
**constant acceleration**, downhill sections represent**constant deceleration**. - Flat sections represent the object travelling at a
**constant speed**. - A curve represents a
**changing acceleration**.

**Distance from a Velocity-Time graph**

Higher tier students need to know how to use **velocity-time **graphs to determine the distance travelled by an object.

We know that \textcolor{00bfa8}{\text{distance} = \text{speed} \times \text{time}}. This corresponds to the area under the velocity-time graph. So the **distance travelled = area under the graph**.

If the area is an irregular shape, it might be easier to count the amount of squares in the area and then multiply this number by the value of 1 square.

For this diagram on the right, the area of the red shaded triangle gives the distance travelled. So the calculation would be:

\text{distance} = \dfrac{1}{2} \times \text{velocity} \times \text{time}

because this gives the area of the triangle.

**Velocity-Time graphs and Terminal Velocity**

Physics students need to know how to interpret** velocity-time** graphs that involve **terminal velocity**.

The **acceleration** of the object decreases as the drag force increases. This is shown where the graph levels out gradually, showing how the object’s acceleration is decreasing. The graph then becomes completely flat, showing the **constant velocity **has been reached. This is the** terminal velocity.**

## Motion Graphs Example Questions

**Question 1**: State which graph that shows an object that starts stationary, accelerates and then travels at a constant speed.

**[1 mark]**

**A B C D**

**D**

The flat horizontal line shows the object is not moving. The upwards curve shows acceleration and the straight steep section shows a constant speed.

**Question 2**: An car travels at a constant velocity of 45 \: \text{m/s}, and then decelerates until it is stationary. Use the velocity-time graph to calculate the distance the car travels.

**[3 marks]**

\text{area of rectangle} = 45 \:\text{m/s} \times 40 \: \text{s} = 1800 \: \text{m} \\ 60 \: \text{s} - 40 \: \text{s} = 20 \: \text{s} \\ \text{area of triangle} = \dfrac{1}{2} \times 45 \: \text{m/s} \times 20 \: \text{s} = 450 \: \text{m} \\ \textbf{total distance} \: \bold{ = 1800 }\bold{ + 450} \\ \bold{= 2250 \:} \textbf{m}

**Question 3**: State what type of motion the object is travelling in. Describe this motion with reference to the graph.

**[4 marks]**

- It is an object reaching it’s
**terminal velocity.** - The
**acceleration of the object decreases as the drag force increases**. This is shown where the**graph levels out**gradually, showing how the object’s acceleration is decreasing. - This acceleration decreases until the
**flat section, which shows a constant velocity**. This is the terminal velocity.

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