Answer
(a) 440 meters
(b) 42 seconds
(c) first second: 21 meters
fifth second: 19 meters
Work Step by Step
(a) Let's convert 75 km/h to units of m/s.
$75 ~km/h ~\times ~ 1000 ~ m/km ~\times ~1 h/3600 s = 21 ~m/s$
To find the distance the car coasts, we can use the equation $v^2= v_0^2 + 2a(x-x_0)$
$x = \frac{v^2 - v_0^2}{2a} = \frac{(-21)^2}{2(-0.50)}= 440 ~m$
(b) To find the time it takes to stop, we use the equation $v - v_0 = at$
Then $t = \frac{v-v_0}{a} = \frac{-21 ~m/s}{-0.50 ~m/s^2} = 42 ~s$
The time it takes to stop is 42 seconds.
(c) The first second is from $t_1 = 0$ to $t_2 = 1$.
$v_1 = 21 ~m/s$ and $v_2 = 21 - (0.50)(1) = 20.5 ~m/s$
The average velocity is $\frac{21+20.5}{2} = 20.75 ~m/s$
$x = 20.75 ~m/s \times 1 s = 21 ~m$
The distance it travels in the first second is 21 meters.
The fifth second is from $t_4 = 4$ to $t_5 = 5$.
$v_4 = 21 - (0.50)(4) = 19 ~m/s$ and $v_5 = 21 - (0.50)(5) = 18.5 ~m/s$
The average velocity is $\frac{19+18.5}{2} = 18.75 ~m/s$
$x = 18.75 ~m/s \times 1 s = 19 ~m$
The distance it travels in the fifthsecond is 19 meters.
Note that the answers are rounded off to two significant digits.
