JEE Advanced (Matrix Match & Integer Answer): Motion | Chapter-wise Tests for JEE Main & Advanced PDF Download

Q.1. An aero plane is moving in the sky and a bag is dropped from t he plane. Let a and v denote the acceleration and velocity of the aero plane. Consider two cases

• a is constant and non zero
• a is zero and plane is moving with uniform velocity

Match the following:-

With a ≠ 0
With respect to plane
dv/dt = g − a which is a constant acceleration
Now since v 0 = 0 with respect to plane.
So it is a straight line
With Respect to ground v ≠ 0 at t=0
Acceleration = g
So it is a parabola
With a = 0 and v ≠ 0
With respect to plane
dv/dt = g which is a constant acceleration
Now since v₀ = 0 with respect to plane.
So it is a straight line
With Respect to ground
v ≠ 0 at t = 0
Acceleration = g
So it is a parabola

Q.2. An object under goes an projectile motion starting from origin with initial velocity Under acceleration due to gravity
H_m  -> Maximum height reached by object
R -> Range of the object
Match the column:

A)-(T);(B)-(S);(C)-(P);(D)-(Q)

Q.3. Match the following

(a) a
(b) b
(c) c
(d) d

Correct Answer is option (a)

Instantaneous speed decreases with time as distance travelled can decrease with time.
In a circular motion, velocity changes as direction of motion changes but speed remains constant for uniformly moving object. Whereas, average velocity changes.
Instantaneous speed is different at different instants/positions, whereas average velocity depends only on initial and final position.
Similarly average speed depends only on initial and final positions and its magnitude can decrease with time. It will also remain constant for a particle moving uniformly in a circle. 

Q.4. Match the following :
A ball is thrown vertically upward in the air by a passenger (relative to himself) from a train that is moving as given in column I (v_ball << v_escape). Correctly match the situation as described in the column I, with the paths given in column II.

(A) q, (B) q , (C) q, (D) q
In all cases, angle between velocity and net force (in the frame of observer) is in between 0° and 180° (excluding both values, in that path is straight line).