Kinematics

Two vectors $\vec A$ and $\vec B$ have equal magnitudes. If magnitude of $\vec A+\vec B$ is equal to two times the magnitude of $\vec A-\vec B$, then the angle between $\vec A$ and $\vec B$ will be :

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 person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

At $t=0$, truck, starting from rest, moves in the positive $x$-direction at uniform acceleration of 5 ms$^{-2}$. At $t=20$ s, a ball is released from the top of the truck. The ball strikes the ground in 1 s after the release. The velocity of the ball, when it strikes the ground, will be :

(Given $g=10$ ms$^{-2}$)

Two projectiles $P_1$ and $P_2$ thrown with speed in the ratio $\sqrt3:\sqrt2$, attain the same height during their motion. If $P_2$ is thrown at an angle of 60° with the horizontal, the angle of projection of $P_1$ with horizontal will be :

A person starts his journey from centre 'O' of the park and comes back to the same position following path OPQO as shown in the figure. The radius of path taken by the person is 200 m and he takes 3 min 58 sec to complete his journey. The average speed of the person is ______ ms$^{-1}$.

(take $\pi=3.14$)

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be :

(Given $\cos135°=-0.7$)

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.

For a free body diagram shown in the figure, the four forces are applied in the '$x$' and '$y$' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero ?

A ball is projected from the ground with a speed 15 ms$^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then '$\tan\theta$' will be equal to :

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$^{-1}$.

Two projectiles thrown at 30° and 45° with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :

If the initial velocity in horizontal direction of a projectile is unit vector $\hat i$ and the equation of trajectory is $y=5x(1-x)$. The $y$ component vector of the initial velocity is ______ $\hat j$.

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

Two projectiles are thrown with same initial velocity making an angle of 45° and 30° with the horizontal respectively. The ratio of their respective ranges will be :

If $\vec A=\left(2\hat i+3\hat j-\hat k\right)$ m and $\vec B=\left(\hat i+2\hat j+2\hat k\right)$ m. The magnitude of component of vector $\vec A$ along vector $\vec B$ will be ______ m.

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 bag is gently dropped on a conveyor belt moving at a speed of 2 m/s. The coefficient of friction between the conveyor belt and bag is 0.4. Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion, is : [Take g = 10 m/s$^{-2}$]

A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown at an angle θ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $\dfrac1x$. The value of $x$ is ______.

A body of mass 10 kg is projected at an angle of 45° with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time $t=\dfrac T{\sqrt2}$, is ______.

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