# Kinematics in One Dimension

## Key Formulas

Δx | displacement | m | |

v_{i} | intitial velocity | m/s | |

Δt | elapsed time | s | |

a | acceleration | m/s^{2} |

v_{f} | final velocity | m/s | |

v_{i} | initial velocity | m/s | |

a | acceleration | m/s^{2} | |

Δx | displacement | m |

## Tips to Remember

- Watch your signs! Objects moving in opposite directions have opposite signs. If a ball starts rolling up a ramp at 3 m/s and later rolls down at 2 m/s, then v
_{i}is 3 m/s, but v_{f}is -2 m/s. If the motion is vertical, it’s best to define upward as positive and downward as negative. This means that the acceleration due to gravity will be -9.8 m/s^{2}, not +9.8 m/s^{2}, because gravity pulls*downward*. Also, an object that ends up at a lower position than it started will have a negative displacement. - Sometimes v
_{i}or v_{f}are zero, but you have to infer that from the information given. For example, “brakes to a stop” indicates that v_{f}is zero. Similarly, “an object falls from a balcony” (as opposed to being thrown) implies that v_{i}is zero. - On the other hand, don’t make the mistake of thinking that an object’s final velocity must be zero because it’s resting on the ground at the end of the problem. If your problem says something like “a ball falls 15 m to the ground,” the final velocity is the velocity the ball had reached at the instant it hit the ground. The final velocity isn’t zero
*until after the ground stops it*, and that’s no longer the same problem!

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