You’re running late to your physics class one day and you need to take the UC sh

Question

You’re running late to your physics class one day and you need to take the UC shuttle. When you turn the corner, you see the shuttle waiting at the stop and you start running towards it. You’re no Usain Bolt, and you’re carrying a backpack (damn heavy with the physics book in it!), so you can only run at a constant speed of 5 m/s. Unfortunately, when you’re only 8 m away from the open door, the shuttle takes off at a constant acceleration of 1 m/s2. Will you manage to catch the shuttle? (Assuming of course that the shuttle driver is nice enough to stop and open the door when he/she sees you.) If you do catch the shuttle, how much do you have to run (distance, time)?'

Explanation / Answer

Yes he will manage to catch the shuttle

in a time t let the shuttle travels a distance s

then in the same time he has to travel a distance of s + 8 to catch the shuttle so

for shuttle

s = 1/2 * a * t^2

s = 1/2 * t^2

for person

s' = 5 * t   ( s' = s + 8)

substituting s from the above equation

0.5 * t^2 - 5t + 8 = 0

we get t = 2 s

and s' = 10 m

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