Question

A scooter increases its speed from $36km/h$ to $72km/h$ in $10s$ . What is its acceleration?
(A) $7.2m/{s^2}$
(B) $1m/{s^2}$
(C) $3.6m/{s^2}$
(D) $10m/{s^2}$

Answer 1

We know that acceleration is nothing but the rate of change in velocity. Also, we know that the first law of kinematics states that $v = u + at$ . Also we know that to convert from $km/h$ to $m/s$ we need to multiply the magnitude of the former by $\dfrac{5}{{18}}$ .

Formulas used: We will be using the formula, that is also called as the Newton’s first equation of kinematics, $v = u + at$ , where $v$ is the final velocity acquired by the body, $u$ is the initial velocity of the body, $a$ is the acceleration achieved by the body, and $t$ is the time taken by the body to achieve the acceleration $a$ .

Complete Step by Step solution
As we know the velocity of a body is the rate of change of displacement, $v = \dfrac{{ds}}{{dt}}$ . Similarly the acceleration the body achieves is the rate of change of velocity, $a = \dfrac{{dv}}{{dt}}$ . Here $dv$ is nothing but change in velocity and $dt$ is nothing but change in time when the body was recorded to be at those velocities.
$\Rightarrow dv = v - u$ where $u$ is the initial velocity and $v$ is the final velocity.
$dt = {t_2} - {t_1}$ where ${t_2}$ is the time at which the body acquires velocity $v$ and ${t_1}$ is the time at which the body acquires velocity $u$ .
Now we know that initial velocity of the body, $u = 36km/h$ and the final velocity of the body, $v = 72km/h$ . We also know that the time required to acquire this change velocity, $dv$ is $dt = {t_2} - {t_1} = 10s$ .
We are required to find the value of acceleration, $a$ . We can also see that the initial and final velocities have different units and we need to convert them from $km/h$ to $m/s$ .
We know that $1km = 1000m$ , also $1hr = 60 \times 60 = 3600s$
$\Rightarrow 1km/h = \dfrac{{1000}}{{3600}}m/s = \dfrac{5}{{18}}m/s$
So, the initial velocity, $u = 36km/hr$ will be $u = (36 \times \dfrac{5}{{18}})m/s$ .
$\Rightarrow u = 10m/s$ .
Similarly, the final velocity, $v = 72km/h$ will be $v = (72 \times \dfrac{5}{{18}})m/s$ .
$\Rightarrow v = 20m/s$ .
Now that we have the values of $v,u$ and $t$ .Let us substitute them in the formula $v = u + at$ .
Substituting, $v = 20m/s$ , $u = 10m/s$ and $t = 10s$ we get, $20 = 10 + a(10)$ .
Subtracting $10$ on both sides,
$10 = 10(a)$
Now by dividing both L.H.S and R.H.S by $10$ we get,
$\Rightarrow a = 1m/{s^2}$ .
Hence the correct answer will be option B.

Note:
Alternate method
Once we find the value of $u = 10m/s$ and $v = 20m/s$ . We know that $a = \dfrac{{dv}}{{dt}}$ .
So, $a = \dfrac{{v - u}}{{{t_2} - {t_1}}}$
$\Rightarrow \dfrac{{20 - 10}}{{10}} = 10m/{s^2}$ .
Thus, the problem can also be solved without using the laws of kinematics.