Kinematics

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The Equation for Speed

This is the rate at which distance is covered by a travelling object.

$$\text{speed}=\frac{\text{distance}}{\text{time taken}}$$

$$v=\frac{\Delta s}{\Delta t}$$

• where
• $v$ is the speed of the object, $m{s}^{-1}$;
• $\Delta s$ is the distance, $m$;
• and
• $\Delta t$ is the time taken to cover the displacement, $s$.

The Rearrangements:

The equation $v=\frac{s}{t}$ can be considered as the average speed over the time interval. This assumes the acceleration during the time interval is zero, that is constant speed, which for many situations works well. For an instantaneous speed we can take the gradient of the displacement-time graph at the time of interest.

Video and Questions:

Speed, distance and time Video:

Practice Questions;

Textbook Exercise.

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The Equation for Acceleration

The rate of change of velocity

$$a=\frac{\Delta v}{\Delta t}$$

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Prerequisites

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Describing the acceleration:

Word equation:

The algebra:

$$a=\frac{\Delta v}{\Delta t}$$

• where
• $a$ is the acceleration of the object, $m{s}^{-2}$;
• $\Delta v$ is the change in velocity, $m{s}^{-1}$;
• and
• $\Delta t$ is the time taken to cover the velocity change in seconds $s$.

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The rearrangements

$$\Delta v=a\Delta t$$ $$A=\frac{B}{C}$$

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Related equations:

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Questions:

Notes and Questions
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Further reading:

Newton's 2^nd Law$$F=ma$$

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Speed versus Time Graphs

A speed versus time graph is the most useful of the kinematics graphs. The acceleration of an object can be found by taking the gradient of a speed versus time graph. The distance travelled can be found from the area between the curve and the time axis.

Area under a Graph Video:

Practice Questions;

Textbook Exercise.

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Velocity Time Graphs:

Velocity Time Graphs;

Solutions.

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Further Reading

Speed and Velocity

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