Motion in a Straight Line Set-2

Q1. A rubber ball is released from a height of $5 \ \mathrm{m}$ above the floor. It bounces back repeatedly, always rising to $81 / 100$ of the height through which it falls. Find the average speed of the ball. (Take $g = 10 \ \mathrm{ms}^{-2}$) [(JEE Main 2021)]

Q2. A car accelerates from rest at a constant rate for some time after which it decelerates at a constant rate to come to rest. If the total time elapsed is $t$ seconds, the total distance travelled is: [(JEE Main 2021)]

Q3. A mosquito is moving with a velocity $\vec{v} = 0.5 t^2 \hat{i} + 3 t \hat{j} \ \mathrm{m/s}$ and accelerating in uniform conditions. What will be the direction of mosquito after $2 \ \mathrm{s}$? [(JEE Main 2021)]

Q4. The trajectory of a projectile in a vertical plane is $y = \alpha x - \beta x^2$, where $\alpha$ and $\beta$ are constants and $x \& y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection and the maximum height attained $H$ are respectively given by: [(JEE Main 2021)]

Q5. A scooter accelerates from rest for time $t_1$ at constant rate $a_1$ and then retards at constant rate $a_2$ for time $t_2$ and comes to rest. The correct value of $t_1/t_2$ will be : [(JEE Main 2021)]

Q6. A stone is dropped from the top of a building. When it crosses a point $5 \ \mathrm{m}$ below the top, another stone starts to fall from a point $25 \ \mathrm{m}$ below the top. Both stones reach the bottom of building simultaneously. The height of the building is : [(JEE Main 2021)]

Q7. An engine of a train, moving with uniform acceleration, passes the signal-post with velocity $u$ and the last compartment with velocity $v$. The velocity with which middle point of the train passes the signal post is : [(JEE Main 2021)]

Q8. A particle moves such that it's position vector is $\vec{r} = A (\cos \omega t \hat{i} + \sin \omega t \hat{j})$, where $\omega$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $\vec{v}$ and acceleration $\vec{a}$ of the particle.

Q9. A particle starts from the origin at $t = 0$ with an initial velocity of $\vec{u} = 10 \hat{j} \ \mathrm{cm/s}$ and moves in the $x-y$ plane with a constant acceleration $\vec{a} = (8 \hat{i} + 2 \hat{j}) \ \mathrm{cm/s}^2$. The $x$-coordinate of the particle at the instant when its $y$-coordinate is $32 \ \mathrm{m}$ is $D \ \mathrm{m}$. The value of $D$ is [Note: Units seem inconsistent in source, solving based on $32 \ \mathrm{m}$ in $\mathrm{cm/s}$ context as given.]

Q10. In a car race on straight road, car A takes a time $t$ less than car B at the finish and passes finishing point with a speed $v$ more than that of car B. Both the cars start from rest and travel with constant acceleration $a_1$ and $a_2$, respectively. Then $v$ is equal to [JEE Main 2019]