Finding velocity of a free-falling object given a function of time

Question

While a man is repairing an elevator that is at rest, its cables

snap and the elevator begins to free fall at t = 0 seconds. At t = 0.5 seconds,

the emergency braking system automatically engages. The mass of the

repairman is mR = 75 kg, and the mass of the elevator car is mE = 200 kg.

The emergency braking system applies a time-dependent braking force, FB ,

in the opposite direction of the elevator car’s motion, where

𝐹𝐵(t) = 600*𝑡^1.5

The units of FB are in newtons (N).

Determine the velocity of the elevator car and repairman at t = 5 seconds.

Answer 1

v₀ = gt₀ = 4.9 m/s; (M+m)g - 600t^1.5 = (M + m)dv/dt; 275g - 600t^1.5 = 275dv/dt;

dv/dt = g - 24/11t^1.5; v = gt - 24/11·t^2.5/2.5 + C; t = 0 v₀ = 4.9; C 4.9 At t = 4.5 s

v = 9.8·4.5 + 4.9 - 24/11·4.5^2.5/2.5 = 11.51 m/s