Question

A particle moves along the x-axis according to the equation $x=6t^2$, where $x$ is displacement in meters and $t$ is time in seconds. Therefore

• A. The acceleration of the particle is $12m{s}^{-2}$
• B. The particle follows a parabolic path
• C. Each second the velocity of the particle changes by $9.8m{s}^{-1}$
• D. The velocity of the particle is $6m{s}^{-1}$ at $t=1.5s$

Answer 1

The correct option is A The acceleration of the particle is $12m{s}^{-2}$

Given,

$x=6t^2$

Velocity, $v=\frac{dx}{dt}$

$v=12t$

$v{|}_{t=1.5s}=12\times 1.3$

$v{|}_{t=1.5s}=18m/s$

Acceleration, $a=\frac{dv}{dt}$

$a=12m/s^2$

The correct option is A.