Motion in a straight line

A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength $1\times10^5$ NC$^{-1}$. If the charge on the particle is 40 $\mu$C and the initial velocity is 200 ms$^{-1}$, how much distance it will travel before coming to the rest momentarily :

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s, the distance travelled by the toy in the next t s will be :

A car is moving with speed of 150 km/h and after applying the break it will move 27 m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ______ m distance.

A particle is moving in a straight line such that its velocity is increasing at 5 ms$^{-1}$ per meter. The acceleration of the particle is ______ ms$^{-2}$ at a point where its velocity is 20 ms$^{-1}$.

A bullet is shot vertically downwards with an initial velocity of 100 m/s from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time t = 20 s will be:

(Take g = 10 m/s$^2$).

A block 'A' takes 2 s to slide down a frictionless incline of 30° and length '$l$', kept inside a lift going up with uniform velocity '$v$'. If the incline is changed to 45°, the time taken by the block, to slide down the incline, will be approximately :

The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at $(4+x)$ cm inside the block. The value of $x$ is :

Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane BC. Time it takes to reach to the point C from point A is $t\left(\sqrt2+1\right)$ s. The value of t is ______.

(use g = 10 m/s$^2$)

A NCC parade is going at a uniform speed of 9 km/h under a mango tree on which a monkey is sitting at a height of 19.6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is :

(Given g = 9.8 m/s$^2$)

A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 J within 1 s, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is

A ball is thrown vertically upwards with a velocity of 19.6 ms$^{-1}$ from the top of a tower. The ball strikes the ground after 6 s. The height from the ground up to which the ball can rise will be $\left(\dfrac k5\right)$ m. The value of k is ______ (use g = 9.8 m/s$^2$)

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height $\dfrac h3$ while going up and coming down respectively.

If $t=\sqrt x+4$, then $\left(\dfrac{dx}{dt}\right)_{t=4}$ is :

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

A ball is released from a height h. If $t_1$ and $t_2$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_1$ and $t_2$.

Two trucks A and B are approaching each other on a straight path with the velocities of 16 m/s and 20 m/s respectively. When they are 200 m apart their drivers see each other and applies the breaks simultaneously. If the truck A decelerates with 2 m/s$^2$ and truck B decelerates with 4 m/s$^2$, what is the distance between them when they finally stop?

A particle of mass $M = 0.2$ kg is initially at rest in the $xy$-plane at a point $(x = -l, y = -h)$, where $l = 10$ m and $h = 1$ m. The particle is accelerated at time $t = 0$ with a constant acceleration $a = 10\ \text{m/s}^2$ along the positive $x$-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by $\vec L$ and $\vec\tau$, respectively. $\hat i$, $\hat j$ and $\hat k$ are unit vectors along the positive $x$, $y$ and $z$-directions, respectively. If $\hat k = \hat i \times \hat j$ then which of the following statement(s) is(are) correct?

A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle 60° with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is $(2 - \sqrt3)/\sqrt{10}$ s, then the height of the top of the inclined plane, in metres, is ______. Take $g = 10\ \mathrm{m\,s^{-2}}$.

A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $x$-axis. Its kinetic energy $K$ changes with time as $dK/dt = \gamma t$, where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m = 0.4$ kg is at rest on this surface. An impulse of 1.0 N s is applied to the block at time $t = 0$ so that it starts moving along the $x$-axis with a velocity $v(t) = v_0 e^{-t/\tau}$, where $v_0$ is a constant and $\tau = 4$ s. The displacement of the block, in metres, at $t = \tau$ is __________. Take $e^{-1} = 0.37$.