#### An Olympic-class sprinter starts a race with an acceleration of 4.50 m/s^{2}.

#### (a) What is her speed 2.40 s later?

#### (b) Sketch a graph of her position vs. time for this period.

**Solution:**

We are given

### Part A

The unknown is v_{f}. The formula in solving for v_{f} is

Substituting the given values,

### Part B

The relationship between position and time can be calculated using the formula

Then, with the given, we can express position in terms of time

The values of the position given the time is tabulated below

Time (s) | Position (m) |
---|---|

0 | 0 |

1 | 2.25 |

2 | 9 |

3 | 20.25 |

4 | 36 |

5 | 56.25 |

6 | 81 |

7 | 110.25 |

8 | 144 |

9 | 182.25 |

10 | 225 |

The values are plotted in the coordinate axes