NEET Physics Oscillations MCQs

A particle moves along the x-axis such that its velocity $v$ varies with time $t$ as $v = At^2 + Bt + C$, where A, B, and C are constants. If the particle starts from rest at $t=0$ and its acceleration at $t=1$ second is $4 m/s^2$, and its velocity at $t=2$ seconds is $8 m/s$, what is the distance traveled by the particle in the first 2 seconds?

A particle moves in a straight line with a velocity given by $v = \alpha t + \beta t^3$, where $\alpha$ and $\beta$ are constants. If its acceleration at $t=1$ second is twice its acceleration at $t=0$, what is the relation between $\alpha$ and $\beta$?

A simple pendulum of length $L$ has a time period $T$. If the length is increased by $\Delta L$ such that $\Delta L << L$, the change in time period $\Delta T$ is approximately:

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 moves along the x-axis with a velocity given by $v = 4t - 2$. What is its acceleration at $t = 2$ seconds?