A bicyclist is finishing his repair of a flat tire when a friend rides by with a constant speed of 3.5 m>s. Two seconds later the bicyclist hops on his bike and accelerates at 2.4 m>s2 until he catches his friend. (a) How much time does it take until he catches his friend

4.28 s

Explanation:

after two seconds (2 s) His friends is

d = 3.5 m/s x 2 s = 7 meter ahead.

in this state, a bicylist start from initial velocity vo = 0 m/s and accelerat 2.4 m/s²

then, when bicylist reach his friend

t friend = t bicyclist = t

d bicylist = d friend + d

d friend = 3.5 . t

d bicylist = vo . t + ½ a t²

d friend + d = vo . t + ½ a t²

3.5 t + 7 = 0 . t + ½ . 2.4 . t²

3.5 t + 7 = 1.2 t²

0 = 1.2 t² - 3.5 t - 7

t = -1.363 and t = 4.28

take the positive one

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