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When Jim and Rob ride bicycles, Jim can only accelerate at three-quarters the acceleration of Rob. Both start from rest at the bottom of a long straight road with a constant upward slope. If Rob takes 5.0 minutes to reach the top, how much earlier should Jim start to reach the top at the same time as Rob?

Answer :

Answer:

46s

Explanation:

displacement = (Initial Velocity)(time) + (1/2)(acceleration)(time^2)

Rob:

Initial Velocity = 0

Time = 5 mins

Acceleration = a

Displacement = (0)(5) + (1/2)(a)(5^2)

D = 12.5a

Since it’s the same road, it’s the same displacement

Jim:

Initial Velocity = 0

Time = ?

Acceleration = (3/4)a

Displacement = 12.5a

12.5a = (0)(?) + (1/2)(3/4)(a)(?^2)

12.5a = (3a/8)(?^2)

33.33 = ?^2

5.7735 = ?

Jim Time = 5.7735

Time Difference = JimTime - RobTime = 0.7735 mins

Convert to secs = 0.7735 x 60 = 46.41 secs

Answer = 46 secs

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