Answer
(a) $a = 3.48~m/s^2$
(b) The elevator's velocity 4.00 seconds later is $15.1~m/s$
Work Step by Step
(a) We can find the net force on the elevator:
$\sum F = F_t-mg$
$\sum F = 33,600~N-(2530~kg)(9.80~m/s^2)$
$\sum F = 8806~N$
We can find the acceleration of the elevator:
$\sum F = ma$
$a = \frac{\sum F}{m}$
$a = \frac{8806~N}{2530~kg}$
$a = 3.48~m/s^2$
(b) We can find the velocity 4.00 seconds later:
$v_f = v_0+at$
$v_f = (1.20~m/s)+(3.48~m/s^2)(4.00~s)$
$v_f = 15.1~m/s$
The elevator's velocity 4.00 seconds later is $15.1~m/s$
