Question

A car starts from rest. It moves with uniform acceleration. In 10 second, it attains a speed of $12$$km/hr$ a straight road. Find its acceleration.

Answer 1

Hint: In this question, we will write the values of variables that are known to us that are $v = 12km/hr$, $u = 0km/hr$, and $t = 10\sec $. Then we use the equation of motion that is $v = u + at$, and after substituting and solving we get acceleration $a = \dfrac{1}{3}m/{s^2}$.

Complete Step-by-Step solution:
First we will write the given values that is
As the car starts from rest, therefore, the initial velocity $u$ equal to $0$ $km/hr = $ $0$$m/s$
The final velocity $v$ equal to $12$ $km/hr = $ $\dfrac{{5 \times 12}}{{18}}$$m/s$$ = \dfrac{{10}}{3}$ $m/s$
The time$t$ equal to $10$ sec
Now we know the three equation of motion that are
$v = u + at$---------------------- (1)
$s = ut + \dfrac{1}{2}a{t^2}$-------------------- (2)
${v^2} - {u^2} = 2as$-------------------- (3)
Now we can see that we have two known values that are $u$,$v$ and $t$ we need to find the acceleration $a$. So we will be using the equation (1) and by substituting the values of $v$,$t$ and $u$ in equation (1) we get
$ \Rightarrow v = u + at$
$ \Rightarrow \dfrac{{10}}{3} = 0 + a \times 10$
$ \Rightarrow \dfrac{{1{0}}}{3} = a \times 1{0}$
$ \Rightarrow a = \dfrac{1}{3}$$m/{s^2} = $ $0.34$$m/{s^2}$
Hence, the acceleration comes out to be $0.34$$m/{s^2}$

Note: For these types of questions we need to recall all three equations of motion that are $v = u + at$, $s = ut + \dfrac{1}{2}a{t^2}$, and ${v^2} - {u^2} = 2as$ . Then depending upon what values are known and what is unknown we will choose one equation and try to find the unknown asked in the question