# Question 829d9

Sep 29, 2015

$\text{320 m}$

#### Explanation:

So, you know that your car starts from rest and moves at a constnt acceleration of ${\text{5 ms}}^{- 2}$ for a total of eight seconds.

Since its movement is restricted to one direction, you can find its speed at the time it stops accelerating

$v = {\underbrace{{v}_{0}}}_{\textcolor{b l u e}{= 0}} + a \cdot {t}_{\text{acc}}$

$v = 5 {\text{m"/"s"^color(red)(cancel(color(black)(2))) * 8color(red)(cancel(color(black)("s"))) = "40 ms}}^{- 1}$

At this point in time, it starts moving with constant speed for a total of

${t}_{\text{const" = t_"total" - t_"acc}}$

${t}_{\text{const" = "12 s" - "8 s" = "4 s}}$

This means that it travelled a distance of

$d = v \cdot {t}_{\text{const" = 40"m"/color(red)(cancel(color(black)("s"))) * 4color(red)(cancel(color(black)("s"))) = "160 m}}$

while it was moving at constant speed.

To get the distance it covered while accelerating, use the equation

${v}^{2} = {\underbrace{{v}_{0}^{2}}}_{\textcolor{b l u e}{= 0}} + 2 \cdot a \cdot d$

d = v^2/(2 * a) = (40^2"m"^color(red)(cancel(color(black)(2)))color(red)(cancel(color(black)("s"^-2))))/(2 * 5color(red)(cancel(color(black)("m")))color(red)(cancel(color(black)("s"^(-2))))) = "1600 m"/10 = "160 m"

The total distance covered was

d_"total" = "160 m" + "160 m" = color(green)("320 m")#