Kinematics

Relative velocity of A with respect to B when they move in the same direction with velocities $V_a$ and $V_b$ is:

A person walks $4 \text{ m}$ North and then $4 \text{ m}$ South. What is the total distance walked?

In a $v-t$ graph, a horizontal line represents:

If a car is traveling at $72 \text{ km/h}$, its speed in $\text{ m/s}$ is:

A particle moves along a straight line. Its velocity at any time $t$ is $v = 4t^3 - 2t$. Its acceleration at $t = 2 \text{ s}$ is:

A body starts from rest and moves with uniform acceleration $a$. The velocity of the body after covering a distance $s$ is $v$. The velocity of the body after covering a distance $2s$ is:

If a particle travels $n$ equal distances with speeds $v_1, v_2, ..., v_n$, then the average speed $V$ is given by:

A particle starts from rest at the origin ($x=0$) and moves along the positive $x$-axis. Its acceleration $a$ varies with position $x$ according to the relation $a = \frac{k}{(x+b)^2}$, where $k$ and $b$ are positive constants. Following the analytical steps shown in the diagram, what is the terminal velocity (the velocity as $x \to \infty$) reached by the particle?

A body is moving with a variable acceleration $a = 3t^2 + 4$. If the body starts from rest, the distance traveled in the first $2$ seconds is:

A point moves in a straight line with velocity $v = v_0 - ax$ where $a$ is a positive constant and $v_0$ is the initial velocity. The distance at which the particle comes to rest is:

The unit of a unit vector is:

Vector subtraction is essentially the addition of a:

The minimum magnitude of the resultant of two forces of $10$ N and $6$ N is:

The maximum magnitude of the resultant of two forces of $7$ N and $3$ N is:

If a vector $\vec{R}$ makes angles $\alpha, \beta, \gamma$ with the $x, y,$ and $z$ axes respectively, then the value of $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$ is:

What is the value of the scalar product $\hat{i} \cdot \hat{j}$?

What is the smallest number of coplanar vectors of unequal magnitudes whose sum can be zero?

A point moves such that its displacement as a function of time is $\vec{s} = t^3\hat{i} + t^2\hat{j}$. The curvature of the path at $t=1$ is proportional to:

If $\vec{A}$, $\vec{B}$ and $\vec{C}$ are three vectors such that $\vec{A} + \vec{B} = \vec{C}$ and $A^2 + B^2 = C^2$, then the angle between $\vec{A}$ and $\vec{B}$ is:

Given $\vec{A} = 3\hat{i} + 4\hat{j}$ and $\vec{B} = 7\hat{i} + 24\hat{j}$. A vector $\vec{C}$ having the same magnitude as $\vec{B}$ and parallel to $\vec{A}$ is:

Which of the following laws is used to find the resultant of two vectors starting from the same point?

The displacement of a particle in uniform circular motion after half a revolution in a circle of radius $R$ is:

If the angular speed of a particle is $10 \, rad/s$ and the radius of the circle is $2 \, m$, what is its linear speed?

A vector that represents the change in position of a particle is called:

A projectile is launched such that the horizontal and vertical components of its initial velocity are $u_x$ and $u_y$. The total time of flight is:

A vector is not changed if:

If a particle moves with constant speed in a circle, its velocity vector and acceleration vector are:

The displacement of a particle is given by $x = a\cos\omega t$ and $y = a\sin\omega t$. The motion of the particle is:

The position of a particle is given by $\vec{r} = 3t\hat{i} + 2t^2\hat{j} + 5\hat{k}$. The path of the particle is a:

A projectile has a range $R$ on a horizontal plane. If $h_1$ and $h_2$ are the maximum heights for the two paths for which the range $R$ is the same, then:

When a projectile is thrown at an angle $\theta$ with the horizontal, the shape of its trajectory (path) is mathematically described as a:

If a projectile has a time of flight $T$, the time taken to reach the maximum height is:

The maximum height reached by a projectile launched vertically upwards with velocity $u$ is:

The horizontal velocity of a projectile:

A body is projected with a velocity $u$ at an angle $\theta$. Its speed when it is at the maximum height is $v$. What is the speed when it is at half its maximum height?

What is the angle of projection for which the horizontal range and the maximum height are in the ratio $4:\sqrt{3}$?

The work done by the force of gravity on a projectile during its entire flight (from ground to ground) is:

A projectile is launched from origin. At $t=1$ s, its position is $(10, 15)$ m. Neglecting air resistance and taking $g = 10$ m/s$^2$, the initial velocity vector is:

If air resistance provides a constant horizontal retardation $a$, the time of flight of a projectile projected at angle $\theta$ is:

A ball is projected from the ground at an angle $\theta$ with velocity $u$. The horizontal distance $x$ from the point of projection where its vertical velocity becomes zero is: