Assertion-Reason questions on distance, displacement, rest, and motion.

Here are the solutions to the Assertion-Reason Based Questions:

7. Assertion (A): There is no difference between distance and displacement.

   • This assertion is false. Distance is a scalar quantity representing the total path length, while displacement is a vector quantity representing the shortest distance from the initial to the final position. They are different concepts. Reason (R): Distance and displacement have same units.
   • This reason is true. Both distance and displacement are measured in units of length, such as meters (m). Since A is false and R is true, the correct option is (d).
   $$\boxed{\text{d) A is false, but R is true.}}$$

8. Assertion (A): When final position of a body coincides with its initial position, the body is at rest.

   • This assertion is false. If a body's final position coincides with its initial position, its displacement is zero. However, the body could have moved along a path and returned to its starting point (e.g., completing a lap on a track), meaning it was in motion and not at rest. Reason (R): This is because distance is scalar and displacement is vector.
   • This reason is true. Distance is a scalar quantity (magnitude only), and displacement is a vector quantity (magnitude and direction). Since A is false and R is true, the correct option is (d).
   $$\boxed{\text{d) A is false, but R is true.}}$$

9. Assertion (A): Uniform circular motion is also called accelerated motion.

   • This assertion is true. In uniform circular motion, the speed of the body is constant, but its direction of motion continuously changes. Since velocity is a vector quantity (having both magnitude and direction), a change in direction means a change in velocity. Any change in velocity implies acceleration (specifically, centripetal acceleration directed towards the center of the circle). Reason (R): Direction of motion changes at every point. So velocity is not constant.
   • This reason is true. As explained above, the continuous change in the direction of motion means the velocity vector is not constant, even if the speed is constant. Since both A and R are true, and R correctly explains why uniform circular motion is accelerated motion, the correct option is (a).
   $$\boxed{\text{a) Both A and R are true and R is correct explanation of A}}$$

10. Assertion (A): The slope of distance time graph gives acceleration of the body.

    • This assertion is false. The slope of a distance-time graph represents the speed of the body, not its acceleration. Acceleration is given by the slope of a velocity-time graph. Reason (R): Greater the slope of distance time graph, more is the speed of the body.
    • This reason is true. A steeper slope on a distance-time graph indicates that the distance covered per unit time is greater, which means the body is moving at a higher speed. Since A is false and R is true, the correct option is (d).
    $$\boxed{\text{d) A is false, but R is true.}}$$