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#	Question	Answer
1	What is a scalar quantity?	A quantity with magnitude only. It is specified completely by a single number along with the proper unit.
2	When are two vectors said to be equal?	When they have the same magnitude and the same direction.
3	What is a null vector (or zero vector)?	A vector with zero magnitude. It is obtained as the sum of two equal and opposite vectors, or by multiplying any vector by zero.
4	How is a vector \(\mathbf{A}\) in the x-y plane expressed in terms of its components?	\(\mathbf{A} = A_x \hat{i} + A_y \hat{j}\).
5	How is a vector \(\mathbf{A}\) expressed in three dimensions in terms of its components?	\(\mathbf{A} = A_x \hat{i} + A_y \hat{j} + A_z \hat{k}\).
6	What is the law of sines for the resultant of two vectors?	\( \frac{R}{\sin\theta} = \frac{A}{\sin\beta} = \frac{B}{\sin\alpha} \).
7	What is the magnitude of the velocity of a particle in terms of its components?	\( v = \sqrt{v_x^2 + v_y^2} \).
8	What is the velocity of a particle moving with constant acceleration \(\mathbf{a}\) at time \( t \)?	\( \mathbf{v} = \mathbf{v}_0 + \mathbf{a}t \).
9	What is the equation of the path of a projectile?	\( y = (\tan\theta_0) x - \frac{g}{2(v_0 \cos\theta_0)^2} x^2 \). It is a parabola.
10	At what angle of projection is the horizontal range of a projectile maximum?	\( 45^\circ \).
11	What is the magnitude of the centripetal acceleration of an object moving with speed \( v \) in a circle of radius \( R \)?	\( a_c = \frac{v^2}{R} \).
12	What is the maximum height attained by a projectile?	\( h_m = \frac{(v_0 \sin\theta_0)^2}{2g} \).
13	What is the SI unit of angular speed?	rad s⁻¹.
14	Is angular velocity a scalar or a vector?	Vector.
15	Is the net acceleration of a particle in circular motion always directed towards the centre?	No. Only in uniform circular motion (constant speed) is the net acceleration directed towards the centre.
16	For any arbitrary motion in space, is the relation \( \mathbf{v}_{\text{average}} = \frac{\mathbf{r}(t_2) - \mathbf{r}(t_1)}{t_2 - t_1} \) always true?	Yes.
17	Is the average speed of an object always greater than or equal to the magnitude of its average velocity over a given time interval?	Yes. The two are equal only if the path length equals the magnitude of the displacement, i.e. the object does not change direction.
18	A motorboat races north at 25 km/h while a water current flows at 10 km/h in a direction 60° east of south. What is the magnitude of the resultant velocity of the boat?	Approximately 22 km/h (using the law of cosines with the 120° angle between the two velocity vectors).
19	What did Galileo state about the horizontal ranges of a projectile launched at elevation angles equally above and below 45°?	"For elevations which exceed or fall short of 45° by equal amounts, the ranges are equal" — since \( \sin(90°+2\alpha) = \sin(90°-2\alpha) \), both equal \( \cos 2\alpha \).
20	A cricket ball is thrown at 28 m s⁻¹ at 30° above the horizontal (g = 9.8 m s⁻²). What is the distance from the thrower to where it returns to the same level?	69 m.
21	Are the components \( A_x \) and \( A_y \) of a vector \( \mathbf{A} \) themselves scalars?	Yes — \( A_x \) and \( A_y \) are real numbers (scalars); it is \( A_x\hat{i} \) and \( A_y\hat{j} \) that are vectors, not \( A_x \) and \( A_y \) alone.
22	A cyclist starts at the centre O of a circular park of radius 1 km, cycles to the edge P, then along the circumference (a quarter circle) to Q, then straight back to O. The round trip takes 10 min. What are the net displacement, average velocity, and average speed?	Net displacement = 0 and average velocity = 0 (back at the start); average speed ≈ 5.95 m s⁻¹ (≈21.4 km/h), from total path length \( 1000 + 500\pi + 1000 \approx 3571\,\mathrm{m} \) over 600 s.
23	For the particle with \( \mathbf{r} = 3.0t\,\hat{i} - 2.0t^2\,\hat{j} + 4.0\,\hat{k} \) m, what are the magnitude and direction of its velocity at \( t = 2.0\,\mathrm{s} \)?	Magnitude ≈ 8.5 m s⁻¹, directed about 69° below the x-axis (since \( \mathbf{v} = 3.0\hat{i} - 8.0\hat{j} \) at \( t = 2.0\,\mathrm{s} \)).
24	(NEET 2022) A ball is thrown at 20 m s⁻¹ at 30° above the horizontal (g = 10 m s⁻²). What is its maximum height?	5 m ( \( h_m = (v_0\sin\theta_0)^2/2g = (20 \times 0.5)^2/20 \) ).
25	(NEET 2013-style) A projectile's velocity at a point A (before the apex) is \( (2\hat{i}+3\hat{j}) \) m/s. What is its velocity at the symmetric point B, at the same height after the apex?	\( (2\hat{i}-3\hat{j}) \) m/s — the horizontal component is unchanged while the vertical component reverses sign, by the symmetry of the parabolic path about its highest point.
26	(NEET 2011) A projectile is launched at 20 m s⁻¹ for maximum range (g = 10 m s⁻²). What is that maximum range?	40 m ( \( R_m = v_0^2/g = 400/10 \) ).
27	(NEET 2007) What angle does a straight path from the origin to the point \( (\sqrt{3}, 3) \) make with the x-axis?	60° ( \( \theta = \tan^{-1}(3/\sqrt{3}) = \tan^{-1}\sqrt{3} \) ).