Kinematics Long Questions

Question 1

Explain how a vector is represented graphically.

Answer:
Draw two perpendicular reference axes and choose a suitable scale. From the origin, draw a straight line in the specified direction. Its length represents the vector's magnitude according to the scale, while the arrowhead shows its direction. For example, if 100 N is represented by 1 cm, a 350 N force is drawn as a 3.5 cm arrow at the given angle.

Question 2

Differentiate between rest and motion, and between speed and velocity.

Answer:
A body is at rest if its position does not change with respect to its surroundings; it is in motion if its position changes continuously. Rest and motion are relative to the observer. Speed is the scalar distance travelled per unit time, whereas velocity is the vector displacement per unit time and therefore includes direction. Both have SI unit m/s.

Question 3

Describe the different types of motion with examples.

Answer:
Motion is mainly translatory, rotatory or vibratory. In translatory motion, every particle moves in the same direction; it may be linear, such as a falling stone, random, such as a flying bee, or circular, such as a ball whirled on a string. In rotatory motion, all points move about a fixed axis, as in a fan. In vibratory motion, a body repeatedly moves to and fro about a mean position, as in a swing.

Question 4

Explain the difference between distance and displacement.

Answer:
Distance is the total length of the actual path followed and is a scalar. Displacement is the shortest straight-line separation from initial to final position, directed toward the final position, and is a vector. Their SI unit is metre. Distance is always greater than or equal to the magnitude of displacement; they are equal only for straight-line motion without reversal.

Question 5

What do the gradients of distance-time and speed-time graphs represent? Explain.

Answer:
For a distance-time graph, gradient = change in distance/change in time, so it gives average speed. A steeper line means greater speed, while a horizontal line represents rest. For a speed-time graph, gradient = change in speed/change in time, so it gives acceleration. An upward straight line shows constant positive acceleration, a horizontal line shows zero acceleration and a downward line shows deceleration.

Question 6

Prove that the area under a speed-time graph equals the distance covered.

Answer:
For constant speed v over time t, the area under the graph is a rectangle: area = v x t, which equals distance. If speed rises uniformly from 0 to v, the area is a triangle: area = 1/2 x t x v. The average speed is v/2, so distance = average speed x time = 1/2 vt. Thus, in both cases, the area under the speed-time graph is numerically equal to distance travelled.

Question 7

How are equations of motion applied to bodies moving under gravity?

Answer:
For straight-line motion with uniform acceleration, use vf = vi + at, S = vit + 1/2 at² and 2aS = vf² - vi². In free fall, replace a with g, approximately 10 m/s² downward. Take g positive when downward is chosen positive. For an object thrown upward, take g negative; at the highest point vf = 0. For an object released from rest, vi = 0.

Question 8

Explain why distance and displacement may or may not be equal in magnitude.

Answer:
They are equal when an object travels in a straight line from its initial to final position without changing direction. If the path is curved or the object reverses direction, distance is greater than displacement. On a round trip, distance is positive but displacement is zero because the initial and final positions coincide.

Question 9

Two guns fire bullets, but the longer barrel gives a lower muzzle velocity than the shorter barrel. In which gun is the bullet's acceleration larger? Explain.

Answer:
Assuming both bullets start nearly from rest and acceleration is uniform, vf² = 2aS. Therefore a = vf²/(2S). The shorter-barrel gun produces a greater final velocity over a smaller distance, so its bullet must have the larger acceleration.

Question 10

The average velocity of a complete trip is positive. Could the instantaneous velocity be negative at some time? Justify.

Answer:
Yes. Positive average velocity means the net displacement over the total time is positive. During part of the trip the object may move in the opposite direction, giving negative instantaneous velocity, provided its overall final displacement remains in the positive direction.