Motion in a straight line practice · Medium

I, II, III and IV. The relative velocity can be greater or less than the individual velocities depending on the direction of motion.

Option B (Displacement of the particle) is correct because the area under the velocity-time graph represents the displacement of the particle.

Option A (Assertion is correct, reason is correct; reason is a correct explanation for assertion) is correct because the area under the velocity-time graph represents displacement, and displacement is a vector quantity, making the vector sum relevant.

Option B (Displacement of the particle) is correct because the area under a velocity-time graph represents the displacement of the particle.

Option D (If Assertion is false but Reason is true) is correct because the distance between two particles moving with constant velocities can change, but their relative motion is indeed uniform.

Option B (200 m) is correct because the maximum height is proportional to the square of the initial velocity.

Option B (8 s) is correct because the relative speed is the sum of the two speeds, and the total distance is the sum of the two lengths.

Option D (None of these) is correct because the calculated time is 5 s, which is not among the provided options.

Option B (If both assertion and reason are true but reason is not the correct explanation of the assertion) is correct because both statements are true, but the reason doesn't explain why the average speed may be equal to the arithmetic mean of individual speeds.

Option D (10 sec) is correct because the relative velocity is the sum of the two speeds, and the time is the length of the train divided by the relative velocity.

Option D (Go on increasing with time) is correct because the velocity's time derivative is positive, indicating increasing velocity.

Option C ($d > \frac{{{{\left( {{v_1} - {v_2}} \right)}^2}}}{{2a}}$) is correct because it represents the condition where the relative velocity is reduced to zero before the cars collide.

Option C (4 s) is correct because it is the time taken by the stone to reach the ground after falling from the balloon.

Option A (A body having zero velocity will not necessarily have zero acceleration) is correct because an object can have zero velocity at an instant while still experiencing acceleration (e.g., at the highest point of a projectile's trajectory).

Option D (Acceleration) is correct because both spheres experience the same acceleration due to gravity, regardless of their mass.

Option B (0 and v/2) is correct because the displacement is zero, making average velocity zero, while average speed is total distance over time, resulting in v/2.