NEET Questions

A particle starts from rest and moves along a straight line with an acceleration given by $a = 6t - 4$, where $a$ is in $m/s^2$ and $t$ is in seconds. At what time is the velocity of the particle zero after the start of motion?

Two balls are projected horizontally from the same height with different initial speeds. Neglecting air resistance, which statement is true about their times of flight?

A projectile is launched at an angle $heta$ with the horizontal with an initial speed $u$. If the horizontal range is $R$ and the maximum height reached is $H$, what is the relationship between $R$, $H$, and $heta$?

A particle moving with uniform acceleration along a straight line covers distances $S_1$ and $S_2$ in successive time intervals $t_1$ and $t_2$. Which equation correctly relates these quantities?

A ball is thrown horizontally from a cliff edge with velocity $v$. Another ball is dropped vertically from the same point at the same time. Which ball has the greater acceleration at any given instant before hitting the ground (neglecting air resistance)?

A body is projected horizontally with a velocity $u$ from a height $h$. If $R$ is the horizontal range and $T$ is the time of flight, which of the following is correct (neglecting air resistance)?

A particle moves along a trajectory defined by $x = t^3 - 6t^2 + 9t + 2$ and $y = t^2 - 2t + 1$, where $x$ and $y$ are in meters and $t$ is in seconds. What is the magnitude of the displacement of the particle between $t=0$ and $t=4$ seconds?

A bee flies in a spiral path described by $r = 2t$ and $heta = \pi t$, where $r$ is in meters, $heta$ is in radians, and $t$ is in seconds. What is the magnitude of the bee's displacement from $t = 0$ to $t = 2$ s?

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

A body travels along a path described by $y = x^2$. What is the ratio of distance to displacement when moving from $(0,0)$ to $(2,4)$?