Answer
(a) $A = 100.0~N$
$B = 12.5~N/s^2$
(b) (i) At t = 0:
$\sum F = 21.6~N$
$a = 2.70~m/s^2$
(ii) At t = 3.00 s:
$\sum F = 134~N$
$a = 16.8~m/s^2$
(c) $a = 26.6~m/s^2$
Work Step by Step
(a) $F = A + Bt^2$
At t = 0:
$F = 100.0~N$
$A + B(0)^2 = 100.0 ~N$
$A = 100.0~N$
At t = 2.00 s:
$F = 150.0~N$
$100.0~N + B(2.00~s)^2 = 150.0 ~N$
$B = \frac{50.0~N}{4.00~s^2} = 12.5~N/s^2$
(b) (i) At t = 0:
$\sum F = F - mg = 100.0~N - (8.00~kg)(9.80~m/s^2)$
$\sum F = 21.6~N$
$\sum F = ma$
$a = \frac{21.6~N}{8.00~kg} = 2.70~m/s^2$
(ii) At t = 3.00 s:
$\sum F = F - mg$
$\sum F = 100.0~N + (12.5~N/s^2)(3.00~s)^2- (8.00~kg)(9.80~m/s^2)$
$\sum F = 134~N$
$\sum F = ma$
$a = \frac{134~N}{8.00~kg} = 16.8~m/s^2$
(c) At t = 3.00 s:
$F = 100.0~N + (12.5~N/s^2)(3.00~s)^2$
$F = 212.5 N$
$F = ma$
$a = \frac{212.5~N}{8.00~kg} = 26.6~m/s^2$
