Idea 11of 11Builds onOne picture, three equationsWhich equation
Two pictures, one join
Speed up, then brake: which equation covers both?
Today you'll discover
- why one equation cannot hold two accelerations
- where the two stages of a trip touch
- how to add the two answers into one
Think firstA cart speeds up for three seconds, then brakes
The cart hits 12 m/s at 3 s, then brakes to rest in 2 s. Which equation gives the distance?
Decide first, then press Next. Find the one velocity both stages share.
A velocity–time graph of a cart that rises from zero to twelve metres per second in three seconds and falls back to zero in two more. After a prediction, the rising stage is read as an area of eighteen metres, the join at twelve metres per second is marked, and the falling stage's area of twelve metres is added. The last step asks what a dragster's two stages share.
See the whole ideathe big idea and the key word, in one place
The big idea
Two pictures joined at one velocity; solve each, add the areas.
For exampleThe dragster: 39 m/s² for 3.0 s reaches 117 m/s over 176 m; the chutes at 60 m/s² need 1.95 s and 114 m more. Total: 290 m in 4.95 s.
About this modelBelow the line means moving the other way, not slowing down.
Below the line means moving the other way, not slowing down.
Ready to use it?
- Split a two-stage motion at its join and find the total distance or time.