Question

An airline reaches its takeoff speed of $163mph$ in $36.2s$ . What is the magnitude of its average acceleration? ( in $m/{s^2}$ )
(a). $3$
(b). $2$
(c). $1$
(d). $4$

Answer 1

In this question, we have been given the speed i.e.
$163mph$ . We have to find the average acceleration in meters per second. So we will first find the change in velocity by converting the speed in meters per second from miles per hour.
And after that we will use the formula to find the average acceleration i.e.
$a = \dfrac{{\vartriangle v}}{{\vartriangle t}}$ .

Complete step-by-step solution:
We know that the acceleration is the ratio of change of velocity per change in time. It is denoted by $a$ and it is measured in the units of
$m/{s^2}$ .
The formula for average acceleration is
$a = \dfrac{{\vartriangle v}}{{\vartriangle t}}$ , where $\vartriangle v$ is the change in velocity and $\vartriangle t$ is the total time over which the velocity is changing.
So to convert $mph$ to $m/s$ we will directly multiply with
$0.447$.
We have change in velocity
$(163 \times 0.447)m/s$ .
It gives us value
$72.9m/s$(approx.)
We have been given the total time travelled i.e.
$36.2s$ .
So we have
$\vartriangle v = 72.9s$ and
$\vartriangle t = 36.2s$ .
By putting the values in the formula we have:
$a = \dfrac{{72.9}}{{36.2}}m/{s^2}$
On simplifying it gives us value
$a = 2m/{s^2}$ .
Hence the correct option is (b) $2$ .

Note: We should note that the value of $1$ mile is
$1.60934km$ .
To convert this in metre we will multiply the value by
$1000$ .
So it gives:
$1.60934 \times 1000 = 1609.34m$ .
Now we will convert one hour to seconds by multiplying with
$60$second.
We have
$1hr = 60 \times 60 = 3600$ seconds.
Now we know that $1mph$ is one mile per hour. It can also be written as
$\dfrac{{1\,mile}}{{1\,hour}}$
We will put the values in metre and seconds as derived above, so it gives:
$\dfrac{{1609.34m}}{{3600s}}$
It gives us value in metre per second i.e.
$0.447m/s$ .
Hence to convert $mph$ into $m/s$ we just multiply by
$0.447$ .