Motion in a straight line practice · Mixed difficulty

Option B (4 m/s) is correct because average velocity is total displacement divided by total time. The displacement is twice the radius.

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 A (increases with time) is correct because the velocity is derived from the displacement equation and shows a linear relationship with time.

Option B (uniformly accelerated motion) is the most appropriate answer, although the question is vague. It implies constant acceleration.

Option C is correct because the assertion is true as displacement-time graph for uniform acceleration is a parabola, but the reason is false because displacement is proportional to the square of time.

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 C (122.5 m) is correct because it is the height from which the stone falls, calculated using the given condition about the distance traveled in the last second.

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 A (50 s) is correct because it is the time interval that satisfies the given distance between the two cars after 2 minutes, considering their acceleration.

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 (36 s) is correct because it is derived from combining the individual speeds of the man and the escalator.

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.

Option C ($\lambda$) is correct because the acceleration is constant and equal to $\lambda$ when calculated from the given velocity equation.