A trolley moves along a rail. A model gives its speed as v(t) = (t² - 7t + 10)/(t - 5) 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 trolley moves along a rail. A model gives its speed as metres per second (m/s), where is the time in seconds. The formula has no value at s, because the bottom is zero there. Find the speed predicted at s. Then find the value that the speed approaches as tends to s.
Need a reminder? The key ideaShow
When substitution gives , factorise or rationalise, cancel the common factor, and substitute again. For divide the top and the bottom by the highest power of , and use .
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.
Given. in m/s, for s.
Plan. Factorise the top, cancel , then substitute.
Step 1. Factorise. . For , .
Step 2. At s. .
Step 3. The limit. As , , so the speed approaches .
Check. The speed at s is a little below m/s, as expected for a point just before s.
Answer: at s, and the speed approaches .
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