Answer
A constant deceleration of $~~-4.82~m/s^2~~$ is required.
Work Step by Step
We can express $100~km/h$ in units of $m/s$:
$(100~km/h)\times \frac{1000~m}{1~km}\times \frac{1~h}{3600~s} = 27.78~m/s$
$a(t) = \frac{dv}{dt} = a$
$v(t) = v_0+a~t$
$s(t) = s_0+v_0~t+\frac{1}{2}at^2$
When $t = 0$, we can let $s = 0$. Then $s_0 = 0$
$s(t) = v_0~t+\frac{1}{2}at^2$
When $s = 80$, we can let $v = 0$
Then $at = -v_0$
We can find $t$ when $s = 80$:
$s(t) = v_0~t+\frac{1}{2}at^2 = 80$
$v_0~t+\frac{1}{2}(-v_0)~t = 80$
$\frac{1}{2}(v_0)~t = 80$
$t = \frac{160}{v_0}$
$t = \frac{160}{27.78}$
$t = 5.76~s$
We can find $a$:
$v(5.76) = v_0+a~t = 0$
$a~t = -v_0$
$a = -\frac{v_0}{t}$
$a = -\frac{27.78}{5.76}$
$a = -4.82~m/s^2$
A constant deceleration of $~~-4.82~m/s^2~~$ is required.
