A cyclist rides along a straight track. At time t seconds her speed is v = 6t² - 4t + 3 metres per…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A cyclist rides along a straight track. At time seconds her speed is metres per second, and at she is from the start. Her distance from the start has the derivative . Find her distance from the start at and at .
Need a reminder? The key ideaShow
An antiderivative of is a function with . The whole family is , and a point on the curve fixes .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Integrate. .
Step 2. Find . At we have .
Step 3. Evaluate. and .
Answer: at and at .
Check. The speed at is , and the distance grows from to in the first second. That fits a speed that starts at and reaches .
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