NEET Physics Oscillations Displacement MCQs

A particle moves along a trajectory defined by $\vec{r}(t) = (2t^3 - 3t^2)\hat{i} + (t^2 - 2t)\hat{j}$, where $t$ is in seconds and $\vec{r}$ is in meters. What is the magnitude of the displacement of the particle between $t = 1\ s$ and $t = 2\ s$?

A car travels 20 km North, then 10 km East, and finally 10 km South. What is the magnitude of the car's displacement?

A particle's position is given by $\vec{r}(t) = 5t\hat{i} + (4t - 3t^2)\hat{j}$. At what time is the displacement vector perpendicular to the velocity vector?

A body moves in a plane such that its displacement vector is given by $\vec{r} = (3t^2 - 2)\hat{i} + (2t^3 + 1)\hat{j}$. At what time is the velocity vector perpendicular to the acceleration vector?

A particle undergoes three consecutive displacements: $\vec{d_1} = 2\hat{i} - \hat{j} + 3\hat{k}$, $\vec{d_2} = -\hat{i} + 2\hat{j} + \hat{k}$, and $\vec{d_3} = x\hat{i} + y\hat{j} - 2\hat{k}$. If the final position of the particle is the same as its initial position, what are the values of $x$ and $y$?

A particle moves in a circle of radius $R$. If it traverses an arc length equal to $\pi R/2$, what is the magnitude of its displacement?

An object completes one full rotation. What is its displacement?

A body moves 6 m North, 8 m East and 10 m vertically upwards. What is the magnitude of its resultant displacement?

A particle moves 5 m East, then 5 m South, then 5 m West, and finally 5 m North. What is its displacement?

A car travels 5 km East and then 3 km West. What is the displacement of the car?