Question

A particle moves in a straight line with a constant acceleration. It changes its velocity from $10$ m/s to $20$ m/s while passing through a distance of $135$ m in t seconds. The value of t is:-

• A. $12$
• B. $9$
• C. $10$
• D. $1.8$

Answer 1

The correct option is B. $9$.

solution

Applying second $e{q}^n$ of motion, we get

$s=ut+\frac{a{t}^2}{2}...\left(i\right)$

Also from first $e{q}^n$ of motion,

we have

$v-u=at$

$\Rightarrow a=\frac{v-u}{t}...\left(ii\right)$

From (i) and (ii), we get

$s=ut+\frac{(v-u)}{2}t$

$\Rightarrow s=\left(\frac{u+v}{2}\right)t$

Here, $135=\left(\frac{10+20}{2}\right)t$

$t=9s$

Thus, option (B) is correct.