Speed Time Graph

Overview

Engineering reference data for Speed Time Graph in chemistry.

Key Formulas

Ideal Gas Law

$PV = nRT$

Pressure × Volume = moles × gas constant × temperature.

Molarity

$M = \frac{n}{V}$

Moles of solute per liter of solution.

pH

$pH = -\log_{10}[H^+]$

Measure of acidity.

Variables

Area Under Velocity-Time Graph

The area under a velocity-time graph represents the total distance traveled. For an object moving with constant velocity over a time interval, the distance is simply the product of that velocity and the time duration.

For an object with varying velocity, the total distance is the sum (integral) of the areas of all rectangles under the graph.

Distance Calculation Example

The following data table corresponds to the example car journey described in the text.

The total distance traveled is calculated as the sum of the areas of the rectangles formed by each interval:

$$\begin{align*} \text{Distance} &= (25 \, \text{m/s} \times 120 \, \text{s}) + (30 \, \text{m/s} \times 220 \, \text{s}) + (15 \, \text{m/s} \times 300 \, \text{s}) \\ &= 3000 \, \text{m} + 6600 \, \text{m} + 4500 \, \text{m} \\ &= 14100 \, \text{m} \end{align*}$$

More generally, for a velocity function $v(t)$, the distance $s$ traveled from time $t_1$ to $t_2$ is given by the definite integral:

$$s = \int_{t_1}^{t_2} v(t) \, dt$$

Interactive Charts

References

• Original Source