Answer
At $t=1s$, the particle is moving along the negative $x$ direction. This is because the displacement is given by the equation $x=4-12t+3t^2$. After differentiating this equation we get velocity, $v = -12+6t$.
At time $t=1s$, velocity $v$ is $-12+6\times(1) = -6ms^{-1}$. This negative velocity implies that the particle is moving in the negative direction of $x$.
Work Step by Step
Step 1: Find the velocity equation by differentiating the given displacement equation.
$$x=4-12t+3t^2$$
$$\implies v = -12+6t$$
Step 2: Plug in the value of time for which you want to calculate the velocity. Here, we want to calculate the velocity of the particle at time $t=1s$. So,
$$v=-12+6\times(1)=-6m/s$$
Step 3: Note the sign of the velocity. Here it is negative which means that the particle is moving along the $-x$ direction.
