Question

A particle moves in a straight line with a constant acceleration. It changes its velocity from $10m{{s}^{-1}}$ to $20m{{s}^{-1}}$ while passing through a distance $135m$ in $t$ second. The value of $t$ is
A. 12
B. 9
C. 10
D. 1.8

Answer 1

Hint: Recall the equations of motion and apply the suitable equations consecutively for finding height attained by the stone and time taken. Equations of motion are as follows:
$v=u+at$
$s=ut+\dfrac{1}{2}a{{t}^{2}}$
${{v}^{2}}={{u}^{2}}+2as$

Complete step by step answer:
Given that,
Initial velocity, $u=10m{{s}^{-1}}$
Final velocity, $v=20m{{s}^{-1}}$
Distance covered, $d=135m$
Firstly, we will calculate acceleration$\left( a \right)$, by applying 3rd equation of motion and after finding acceleration, we will calculate time $\left( t \right)$ by applying 1st equation of motion.
Now, on applying 3rd equation of motion,

& \Rightarrow {{v}^{2}}={{u}^{2}}+2as \\\ & \Rightarrow {{\left( 20 \right)}^{2}}={{\left( 10 \right)}^{2}}+2\times \left( a \right)\times \left( 135 \right) \\\ & \Rightarrow 400=100+270a \\\ & \Rightarrow 270a=400-100 \\\ & \Rightarrow 270a=300 \\\ & \Rightarrow a=\dfrac{300}{270} \\\ & \Rightarrow a=\dfrac{10}{9}m{{s}^{-2}} \\\ \end{aligned}$$ We found that the acceleration of the particle will be $$\dfrac{10}{9}m{{s}^{-2}}$$. Now for calculating time $$\left( t \right)$$, On applying 1st equation of motion, $$\begin{aligned} & \Rightarrow v=u+at \\\ & \Rightarrow 20=10+\left( \dfrac{10}{9} \right)\times t \\\ & \Rightarrow \dfrac{10t}{9}=\left( 20-10 \right) \\\ & \Rightarrow \dfrac{10t}{9}=10 \\\ & \Rightarrow t=9s \\\ \end{aligned}$$ Hence, the correct option is B, i.e., 9 Additional Information: (1). Students should proceed in the following manner for solving problems related to the equation of motion: (2). Read the question carefully to identify the given quantities and note them. Identify the equation to use and note them. (3). Ensure that all the values are in the same system of measurement and put them in identified equations. (4). Calculate the answer carefully and check the final units. Note: Students should memorize the three equations of motion and understand the physical significance of these equations. Students need to know how to apply the suitable equation of motion on the basis of given data. Students should ensure that all the quantities are in the same system of measurement i.e., S.I., M.K.S., C.G.S. etc.