**1. What is a frame of reference?**

**Answer:** A frame of reference is a coordinate system used to describe the position, orientation, and motion of objects. It serves as a reference point for measuring and observing physical phenomena.

**2. Define motion in a straight line.**

**Answer:** Motion in a straight line, or linear motion, is when an object moves along a straight path with its displacement occurring in a single dimension.

**3. What is a position-time graph?**

**Answer:** A position-time graph shows how the position of an object changes over time. The slope of the graph represents the velocity of the object.

**4. Differentiate between speed and velocity.**

**Answer:** Speed is a scalar quantity that represents the rate of motion (distance traveled per unit time), while velocity is a vector quantity that includes both the speed and direction of motion.

**5. Explain uniform and non-uniform motion.**

**Answer:** Uniform motion occurs when an object moves at a constant speed in a straight line. Non-uniform motion occurs when an object’s speed or direction changes over time.

**6. What is average speed?**

**Answer:** Average speed is the total distance traveled divided by the total time taken. It does not account for variations in speed during the journey.

**7. Define instantaneous velocity.**

**Answer:** Instantaneous velocity is the velocity of an object at a specific moment in time. It is the slope of the position-time graph at a particular point.

**8. What characterizes uniformly accelerated motion?**

**Answer:** Uniformly accelerated motion occurs when an object’s velocity changes at a constant rate. The acceleration remains constant over time.

**9. How is a velocity-time graph interpreted?**

**Answer:** A velocity-time graph shows how an object’s velocity changes over time. The slope of the graph represents the object’s acceleration, and the area under the curve represents the object’s displacement.

**10. What information does a position-time graph provide for uniformly accelerated motion?**

**Answer:** For uniformly accelerated motion, the position-time graph is a parabola. The shape of the graph indicates constant acceleration, and the curvature shows how the position changes non-linearly over time.

**11. Define scalars and vectors.**

**Answer:** Scalars are quantities that have magnitude only, such as distance, speed, and time. Vectors are quantities that have both magnitude and direction, such as displacement, velocity, and force.

**12. Explain vector addition and subtraction.**

**Answer:** Vector addition involves combining two or more vectors to produce a resultant vector, using either the head-to-tail method or parallelogram method. Vector subtraction involves finding the vector difference, often done by adding the negative of the vector to be subtracted.

**13. What are scalar and vector products?**

**Answer:** The scalar product (dot product) of two vectors results in a scalar and is calculated as the product of the magnitudes of the two vectors and the cosine of the angle between them. The vector product (cross product) results in a vector perpendicular to the plane containing the two original vectors, with magnitude equal to the product of their magnitudes and the sine of the angle between them.

**14. Define a unit vector.**

**Answer:** A unit vector is a vector with a magnitude of one, used to indicate direction. It is often denoted by a hat symbol, such as i^\hat{i}i^, j^\hat{j}j^, or k^\hat{k}k^.

**15. How is a vector resolved into components?**

**Answer:** A vector is resolved into components by projecting it onto the coordinate axes. For a vector in two dimensions, this involves finding the horizontal (x) and vertical (y) components using trigonometric functions.

**16. What is relative velocity?**

**Answer:** Relative velocity is the velocity of one object as observed from another object. It is calculated by subtracting the velocity vector of the observer from the velocity vector of the object being observed.

**17. Describe motion in a plane.**

**Answer:** Motion in a plane involves movement in two dimensions, requiring both x and y coordinates to describe the position of an object. This type of motion can be analyzed using vector components.

**18. What is projectile motion?**

**Answer:** Projectile motion is the two-dimensional motion of an object under the influence of gravity, typically involving a horizontal component with constant velocity and a vertical component with constant acceleration due to gravity.

**19. Explain uniform circular motion.**

**Answer:** Uniform circular motion occurs when an object moves in a circular path at a constant speed. The direction of the velocity changes continuously, resulting in centripetal acceleration directed toward the center of the circle.

**20. How are the kinematic equations for uniformly accelerated motion derived?**

**Answer:** The kinematic equations for uniformly accelerated motion are derived from the definitions of velocity and acceleration, integrating the acceleration to find velocity, and integrating the velocity to find displacement. The key equations are:

where u is the initial velocity, v is the final velocity, aaa is the acceleration, t is the time, and sss is the displacement.