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**Definition**: **Instantaneous velocity** is defined mathematically:

v
| (2) |

t(s) | x(m) |

1.00 | 1.00 |

1.01 | 1.02 |

1.10 | 1.21 |

1.20 | 1.44 |

1.50 | 2.25 |

2.00 | 4.00 |

3.00 | 9.00 |

Find the runner's instantaneous velocity at *t* = 1.00 s.
As a first estimate, find the average velocity for the total observed part of
the run. We have,

= = = 4 m/s.
| (3) |

= = = 2 m/s.
| (4) |

We can interpret the instantaneous velocity graphically as follows. Recall
that the average velocity is the slope of the line joining P and Q (from Figure
2.1). To get the instantaneous velocity we need to take
*t* 0, or P Q.
When P Q, the line joining P and Q approaches the tangent to
the curve at P (or Q). Thus the slope of the tangent at P is the instantaneous
velocity at P. Note that if the trajectory were a straight line, we would get
*v* = , the same for all *t* .

**Note: **

- Instantaneous velocity gives more information than average velocity.
- The magnitude of the velocity (either average or instantaneous) is
referred to as the
**speed**.

10/9/1997