Question #829d9

So, you know that your car starts from rest and moves at a constnt acceleration of `"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)_(color(blue)(=0)) + a * t_"acc"`

`v = 5"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_"const" = t_"total" - t_"acc"`

`t_"const" = "12 s" - "8 s" = "4 s"`

This means that it travelled a distance of

`d = v * t_"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)_(color(blue)(=0)) + 2 * a * 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")`