Question

A car, initially traveling at 2.0 miles per hour, comes to rest in 8.6 s. What was its acceleration in this time?

Answer 1

Given:

the speed of the car is

$u=2.0\text{ mi/h}$

Time during which it comes to rest

$t=8.6\text{ s}$

Required: acceleration is to be calculated

Explanation:

first, convert the speed from miles per hour to meters per second

in doing so we use a conversion factor

that is given as

$1\text{ mi/h= 0.447 m/s}$

Then the speed is ,

$\begin{gathered} u=2.0\text{ }\times0.447 \\ u=0.894\text{ m/s} \end{gathered}$

now calculate the acceleration,

we know that

$v=u+at$

where v is the final velocity that is zero because finally, the car comes to rest.

plugging all the values in the above relation, we get

$\begin{gathered} 0=0.894\text{ m/s }+a\times8.6\text{ s} \\ a=-\frac{0.894}{8.6} \\ a=-0.10\text{ m/s}^2 \end{gathered}$

negative sign shows that acceleration in the opposite direction

Thus, the acceleration is

$0.10\text{ m/s}^2$