Question

A car traveling 31 mi/h accelerates uniformly

for 6 s, covering 401 ft in this time.
What was its acceleration? Round your
answer to the nearest 100th place.
Answer in units of ft/s?.

Answer 1

Answer:
`a=7.12\ (ft)/(s^2)`

Step-by-step explanation:

For this exercise we need to use th following formula:

`d=V_0t+(1)/(2)at^2`

Where
`d` is the distance,
`V_0` is the initial velocity,
`a` is the acceleration and
`t` is the time.

The first step is to convert from
`31 (mi)/(h)` to
`(ft)/(s)`. Since:

`1\ mi=5,280\ ft\\\\1\ h=3,600\ s`

We get:

`(31 (mi)/(h))((5,280\ ft)/(1\ mi))((1\ h)/(3,600\ s))=45.466\ (ft)/(s)`

Knowing that:

`V_0=45.466\ (ft)/(s)\\\\t=6\ s\\\\d=401\ ft`

We can substitute values into the formula and solve for "a":

`401=(45.466)(6)+(1)/(2)a(6)^2\\\\401=272.796+18a\\\\401-272.796=18a\\\\a=(128.204)/(18)\\\\a=7.122\ (ft)/(s^2)`

Rounded to the nearest 100th place:

`a=7.12\ (ft)/(s^2)`