Question

Velocity and acceleration of a particle at some instant of time are $v=(3\hat{i}+4\hat{j}){ms}^{-1}$ and $a=-(6\hat{i}+8\hat{j}){ms}^{-2}$ respectively. At the same instant particle is at origin. Maximum x-coordinate of particle will be

• A. $1.5m$
• B. $0.75m$
• C. $2.25m$
• D. $4m$

Answer 1

The correct option is B $0.75m$

X-direction :

Initial velocity $u=3m/s$

Acceleration $a=-6m/s^2$

Final velocity $v=u+at$

For final velocity to be zero, i.e. $v=0$

Or $0=3-6t$

$⟹t=0.5s$

Maximum x-co ordinate $x=ut+\frac{1}{2}a{t}^2$

$⟹x=3\times 0.5+\frac{1}{2}(-6)(0.5{)}^2=0.75m$