List of top Physics Questions on Motion in a plane

A particle moves along a parabolic path $y = 9x^2$ in such a way that the x-component of velocity remains constant. If the total acceleration of the particle is $2\hat{j}\text{ m s}^{-2}$, find the x-component of velocity.

The equation of path of a projectile moving in x-y plane is given by $ y = x - \frac{x^2}{25} $, then the initial speed and maximum height of particle will be (take $ g = 10 \, \text{m/s}^2 $):

The magnitudes of three vectors \(\vec A,\vec B,\vec C\) are \(12,5\), and \(13\) units respectively and \(\vec A+\vec B=\vec C\). The angle between \(\vec A\) and \(\vec B\) is

An aeroplane is moving in a circular path with a speed of \(450\ \text{kmph}\). What is the change in velocity in half revolution?

If \(|\vec A+\vec B|=|\vec A-\vec B|\), then the angle between the two vectors \(\vec A\) and \(\vec B\) is

The ratio between maximum and minimum values of two vectors \(\vec A\) and \(\vec B\), where \(A>B\), is \(4:1\). Then the ratio between the magnitudes of two vectors is

If the velocity (in \( \text{m s}^{-1} \)) of a particle at any instant \( t \) is given by \( 2.0\hat{i} + 3.0t\hat{j} \), then the magnitude of its acceleration (in \( \text{m s}^{-2} \)) is

If \(A+B=C\) and \(A^2+B^2=C^2\), then the angle between vectors \(A\) and \(B\) is

The area of rectangle with sides as \(\vec A=3\hat i+4\hat j\) and \(\vec B=\hat i+3\hat j\) is

If \(A+B=C\) and \(A^2+B^2=C^2\), then the angle between vectors \(A\) and \(B\) is

The area of rectangle with sides as \(\vec A=3\hat i+4\hat j\) and \(\vec B=\hat i+3\hat j\) is

Two vectors are given by $\vec{A} = \hat{i} - 2\hat{j} + 3\hat{k}$ and $\vec{B} = 2\hat{i} - 4\hat{j} + 3\hat{k}$. The unit vector along $\vec{A} + \vec{B}$ is

The vertical displacement (y in metre) of a projectile in terms of its horizontal displacement (x in metre) is given by $y=(\sqrt{3}x - 0.2x^2)$. The time of flight of the projectile is (Acceleration due to gravity = 10 ms$^{-2}$)

A ball projected at an angle of 45$^\circ$ with the horizontal crosses two points at equal heights separated by a distance at times 2 s and 8 s respectively. The horizontal distance between the two points is (Acceleration due to gravity = 10 ms$^{-2}$)

If a body projected with a velocity of 19.6 ms⁻¹ reaches a maximum height of 9.8 m, then the range of the projectile is (Neglect air resistance)

A person travelling on a straight line moves with a uniform velocity \( v_1 \) for a distance \( x \) and with a uniform velocity \( v_2 \) for the next \( \frac{3x}{2} \) distance. The average velocity in this motion is \( \frac{50}{7} \, \text{m/s} \). If \( v_1 \) is 5 m/s, then \( v_2 \) is ___ m/s.

If two vectors \(\vec{A}\) and \(\vec{B}\) having equal magnitude \(R\) are inclined at an angle \(\theta\), then

The resultant of two vectors \( \vec{A} \) and \( \vec{B} \) is perpendicular to \( \vec{A} \) and its magnitude is half that of \( \vec{B} \). The angle between vectors \( \vec{A} \) and \( \vec{B} \) is ________ .

A bullet is fired from a gun at the speed of 280 ms^-1 in the direction 30° above the horizontal. The maximum height attained by the bullet is
(g = 9.8 ms^-2, sin 30° = 0.5)

A particle moves in a circular path with uniform speed v. When it turns by 90°, find ratio of \(\frac{v}{<\overrightarrow{v}>}\)?

Two forces of magnitude A and \(\frac{A}{2}\) act perpendicular to each other. The magnitude of the resultant force is equal to:

Two projectiles u₁ and u₂, with speed of 40 m/s and 60 m/s respectively are thrown at a certain angle, u₁ with 30^o and u₂ with 60^o, what is the ratio of range?