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's velocity is given by $v = 4 - 2t$, where $t$ is in seconds and $v$ is in m/s. If the particle starts at $x = 2$ m at $t = 0$, at what time does the particle instantaneously change its direction of motion?

A ball is thrown vertically upwards. Which of the following graphs correctly represents the variation of acceleration with time during its upward motion (neglecting air resistance)?

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 $\beta$?

Two cars, A and B, start from rest at the same point. Car A moves with constant acceleration 'a' and car B moves with constant acceleration '2a'. After how much time will the distance between them be 'S'?

A particle is projected vertically upwards with an initial speed 'u'. At a height 'h' above the ground, its speed is 'v'. What is the maximum height reached by the particle?

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 body moving with a constant velocity has:

The position vector of a particle $\vec{R}$ as a function of time is given by: $\vec{R} = 6\sin(2\pi t)\hat{i} + 6\cos(2\pi t)\hat{j}$. Where R is in meters, t is in seconds and $\hat{i}$ and $\hat{j}$ denote unit vectors along x- and y-directions, respectively. Which one of the following statements is wrong for the motion of the particle?

A particle moves in the x-y plane with its position vector given by $\vec{R} = 4\sin(\pi t)\hat{i} + 4\cos(\pi t)\hat{j}$, where R is in meters and t is in seconds. Which of the following is incorrect?