The numerical ratio of displacement to the distance covered is always

When are the path length and the magnitude of displacement the same?

Why is a frame of reference required?

The position of a particle along the $x$-axis at time $t$ is given by $x = 2 + t - 3t^2$. The displacement and the distance travelled in the interval $t = 0$ to $t = 1$ are respectively:

When is an object said to be in motion? What is meant by the description of an object's motion?

The position vector of a particle is given by the expression $\vec{r} = 3t^2 \hat{i} + 4t^2 \hat{j} + 7 \hat{k}$. The distance traversed in the first $10 \, s$ is ......... $m$.