Answer
(a) $5~s$
(b) My speed is $8~m/s$
(c) $0.94~s$
Work Step by Step
(a) $v_0=16~m/s$, $v=0$, $a=-3.2~m/s^2$
$v=v_0+at$
$0=(16~m/s)+(-3.2~m/s^2)t$
$t=\frac{16~m/s}{3.2~m/s^2}=5~s$
(b) My speed is $8.0~m/s$
$t=\frac{5~s}{2}=2.5~s$
$v=v_0+at$
$v=(16~m/s)+(-3.2~m/s^2)(2.5~s)$
$v=(16~m/s)-(8m/s)=8~m/s$
(c) Place the origin at the starting position ($x_0=0$)
$x=x_0+v_0t+\frac{1}{2}at^2$
$x=0+(16~m/s)(5~s)+\frac{1}{2}(-3.2~m/s^2)(5~s)^2$
$x=40~m$
After applying the brakes, the car runs 40 m until it stops. But, $55~m-40~m=15~m$. The driver must apply the brakes before his car runs 15 m.
$x=x_0+vt$
$15~m=0+(16~m/s)t$
$t=\frac{15~m}{16~m/s}=0.94~s$
