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Peter's Index Physics Home Lecture 1 Course Index Lecture 2a

Bridging Course - Lecture 2 (acceleration and speed)

The techniques of finding slopes (how quickly something changes in time or space) and finding areas (the effect of something through time or space) will now be extended to speed and acceleration.

In this lecture the following are introduced:

• Average and instantaneous acceleration

• Speed vs time graph to acceleration vs time graph

• Acceleration vs time graph to speed vs time graph

• Constant acceleration graphs and equations

Definition of average acceleration

This will have the S.I. unit of m.s |

Definition of instantaneous acceleration

The By working out the slopes at every point on a speed vs time graph, we can construct the corresponding instantaneous acceleration vs time graph. |

Instantaneous acceleration and the speed vs time graph

At t |

Finding the speed vs time graph from the acceleration vs time graph.

The area under the acceleration vs time graph gives the effect of acceleration through time, i.e. it give the speed change.

Example 5

An object accelerates from zero speed at its origin and at a constant rate of 3 m.s^{-2}.
Find the speed and position as functions of time while it continues at this rate.

A change in a quantity is signalled by a triangle Δ which is really "Delta", the capital "D" in Greek.
The area under the acceleration vs time graph gives the effect of acceleration through time,
which is a speed change and written as Δv. |

Position-Speed-Acceleration graphs summary.

The blue slope line on the position vs time graph gives the instantaneous speed
which is the blue vertical arrow in the speed vs time graph below it. |

Example 6

A car is at its origin at time t=0s. It then has a speed given by v = 5 + 10t m.s^{-1}.
Find the acceleration and position at 3s.

The speed vs time graph is: |

The rectangle represents the change in position that would have occured if the car continued at its initial speed.

The triangle represents the additional distance that was added by the acceleration.

Since the car started from the origin, the final position is simply the change in position.

Constant acceleration graphs and equations

When a body has constant acceleration "a", the following applies.

Constant acceleration under gravity

The Earth's force of gravity pulls mass towards it centre.
Near the earth's surface, gravity causes masses to accelerate downwards with a constant value of 9.8 m.s^{-2}.
Using "g" as the symbol for this uniform acceleration, the following applies.

*Summarising:*

Instantaneous positions, speeds and accelerations. |
When a body has constant acceleration "a", the following applies. |

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