A UCI student is running at her top speed of 5.1 m/s to catch a Shuttle bus, which is stopped at the bus stop. When the student is still a distance 42.0 m from the Shuttle bus, it starts to pull away, moving with a constant acceleration of 0.163 m/s2 .For how much time does the student have to run at 5.1 m/s before she overtakes the bus?

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A UCI student is running at her top speed of 5.1 m/s to catch a Shuttle bus, which is stopped at the bus stop. When the student is still a distance 42.0 m from the Shuttle bus, it starts to pull away, moving with a constant acceleration of 0.163 m/s2 .For how much time does the student have to run at 5.1 m/s before she overtakes the bus?

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Step 1

Let us say that the student overtakes the bus after ‘t’ seconds.

Now the distance travelled by the bus in t seconds will be:

Step 2

In the same time, the student travels ‘s’ meters:

Step 3

From Eq1 and Eq2...

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