Question

The position coordinate of a particle moving along a straight line is given by $x=4t^3$ - $3t^2$ + $4t$ + $5$. Then when velocity be equal to zero ?

• A. $t=1$
• B. $t=2$
• C. $t=4$
• D. Cannot be zero

Answer 1

Answer: (D)

Cannot be zero

$x\left(t\right)=4t^3-3t^2+4t+5$

On differentiation w.r.t. time we get the velocity of the particle as a function of time.

$v\left(t\right)=\frac{dx}{dt}=12t^2-6t+4$.

To find when the velocity will be 0, we have to find the roots of the above expression.

Discriminant of the quadratic expression, $D={\left(6\right)}^2-4\left(12\right)\left(4\right)=36-192=-156$.

$D<0$

$\therefore$ The quadratic equation has no real roots.

$\therefore$ Velocity of the particle cannot be 0.