Motion in a straight line

The time taken by a block of mass $m$ to slide down from the highest point to the lowest point on a rough inclined plane is 50 % more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at 45° with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is ________.

From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is ________ m.
(Take $g=10$ m/s² and neglect the air resistance)

The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is ________ m/s. Assume pulley is massless and string is light and inextensible. (Take $g=10$ m/s²)

A block takes $t$ time to slide down a plane inclined at 45° to the horizontal. If the surface is made smooth (frictionless), the block takes time $\dfrac t2$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\left(\dfrac\alpha{100}\right)$. The value of $\alpha$ is ________.

A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ________ m. (Take $g=10$ m/s²)

Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of 5 m/s and 12 m/s, respectively. The distances traversed by the masses in the 5th second are 104 m and 129 m, respectively. The ratio of their momenta after 10 s is $\dfrac x8$. The value of $x$ is ________.

The maximum speed in $\mu$m/s at which the $8^{\text{th}}$ bright fringe will move is _____.

A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is $60\ \mathrm{cm\,s^{-1}}$, the speed of the tip of the person's shadow on the ground with respect to the person is _____ $\mathrm{cm\,s^{-1}}$.

A thin circular coin of mass 5 gm and radius $4/3$ cm is initially in a horizontal $xy$-plane. The coin is tossed vertically up ($+z$ direction) by applying an impulse of $\sqrt{\dfrac\pi2}\times10^{-2}$ N-s at a distance $2/3$ cm from its center. The coin spins about its diameter and moves along the $+z$ direction. By the time the coin reaches back to its initial position, it completes $n$ rotations. The value of $n$ is _____.

[Given: The acceleration due to gravity $g = 10\ \mathrm{m\,s^{-2}}$]

A block of mass 10 kg starts sliding on a surface with an initial velocity of $9.8\ \mathrm{ms^{-1}}$. The coefficient of friction between the surface and block is 0.5. The distance covered by the block before coming to rest is :

[use $g=9.8\ \mathrm{ms^{-2}}$]

From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach the ground in ______ s.

An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use $g=10\ \mathrm{ms^{-2}}$].

Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by $X_P(t)=\alpha t+\beta t^2$ and $X_Q(t)=ft-t^2$. At what time, both the buses have same velocity ?

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero ?

A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is ______ m.

[Use $g=10$ m/s$^2$]

A ball is projected vertically upward with an initial velocity of 50 ms$^{-1}$ at $t=0$ s. At $t=2$ s, another ball is projected vertically upward with same velocity. At $t=$ ______ s, second ball will meet the first ball ($g=10$ ms$^{-2}$).

When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity $v$ and then sinks to the bottom with the constant velocity $v$. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

A ball is spun with angular acceleration $\alpha=6t^2-2t$ where $t$ is in second and $\alpha$ is in rads$^{-2}$. At $t=0$, the ball has angular velocity of 10 rads$^{-1}$ and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :

A car covers AB distance with first one-third at velocity $v_1$ ms$^{-1}$, second one-third at $v_2$ ms$^{-1}$ and last one-third at $v_3$ ms$^{-1}$. If $v_3=3v_1$, $v_2=2v_1$ and $v_1=11$ ms$^{-1}$ then the average velocity of the car is ______ ms$^{-1}$.

Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at $t=0$ s. Ball B is thrown vertically down with an initial velocity '$u$' at $t=2$ s. After a certain time, both balls meet 100 m above the ground. Find the value of '$u$' in ms$^{-1}$. [use $g=10$ ms$^{-2}$] :