Motion | Jamb(UTME)

Types of Motion

1. Motion is the change in an object’s position over time.
2. Translational motion occurs when an object moves from one place to another.
3. Rotational motion happens when an object spins around a fixed axis (e.g., a spinning wheel).
4. Oscillatory motion is repetitive back-and-forth movement (e.g., a pendulum).
5. Linear motion occurs when an object moves in a straight line.
6. Circular motion happens when an object moves in a circular path (e.g., the Earth's orbit around the Sun).
7. Periodic motion repeats at regular intervals (e.g., a swinging pendulum).
8. Random motion has no predictable pattern (e.g., motion of gas particles).
9. Motion can be classified as uniform (constant speed) or non-uniform (changing speed).
10. The type of motion depends on the forces acting on the object.
    paragraph

Relative Motion

11. Relative motion describes the movement of an object as observed from another moving object.
12. It depends on the reference frame chosen for observation.
13. The relative velocity of object A with respect to B is: $\vec{v}_{AB}$ = $\vec{v}_A$ - $\vec{v}_B$
14. If two objects move in the same direction, their relative velocity is the difference in their speeds.
15. If two objects move in opposite directions, their relative velocity is the sum of their speeds.
16. Relative motion is crucial in understanding collisions and overtaking scenarios.
17. For objects moving perpendicularly, the relative velocity involves solving a right triangle.
18. Relative motion simplifies complex problems by focusing on the motion between objects.
19. It is widely used in navigation, aviation, and astronomy.
20. Understanding relative motion is essential for solving real-world problems like crossing a river with a current.
    paragraph

Causes of Motion

21. Motion occurs when a force acts on an object.
22. Force is any push or pull that causes a change in motion or shape.
23. The greater the force applied, the greater the change in motion.
24. Newton’s First Law states that an object remains at rest or in uniform motion unless acted upon by a force.
25. Newton’s Second Law relates force to mass and acceleration: F = ma
26. Newton’s Third Law explains that every action has an equal and opposite reaction.
27. Friction can oppose motion and slow down objects.
28. Gravity causes objects to fall and gives weight to objects.
29. Applied forces like pushing, pulling, or lifting initiate motion.
30. Elastic forces, like those in springs, can also cause motion when released.
    paragraph

Types of Force

31. Contact forces occur when objects physically interact (e.g., friction, tension).
32. Frictional force opposes the motion of objects sliding past each other.
33. Tension force occurs in strings, ropes, or cables under stretching.
34. Normal force acts perpendicular to a surface supporting an object.
35. Non-contact forces act at a distance (e.g., gravitational, magnetic, and electrical forces).
36. Gravitational force pulls objects toward each other (e.g., Earth's gravity).
37. Magnetic force occurs between magnets or magnetic materials.
38. Electrostatic force occurs between charged particles.
39. Applied force is any external push or pull acting on an object.
40. Centripetal force keeps an object moving in a circular path.
    paragraph

Numerical Problems on Collinear Motion

41. Collinear motion involves objects moving along the same straight line.
42. The relative velocity of two objects in collinear motion depends on their directions.
43. Example 1: Two cars are moving in the same direction.
    paragraph
    Car A: $v_A$ = $60 km/h$
    paragraph
    Car B: $v_B$ = 40 km/h
    paragraph
    Relative velocity:
    paragraph
    $v_{AB} = v_A - v_B$ = 60 - 40 = 20 km/h
44. Example 2: Two cars move toward each other.
    paragraph
    
    Car A: $v_A = 50$ km/h
    paragraph
    Car B: $v_B = 30$ km/h
    paragraph
    Relative velocity:
    $v_{AB} = v_A + v_B$ = 50 + 30 = 80 km/h
45. Example 3: A train moves at 90km/h, and a passenger walks at 5km/h in the same direction.
    
    paragraph
    Relative velocity:
    
    paragraph
    $v_{relative}$ = 90 - 5 = 85 km/h
46. Example 4: A bus moves at 60, km/h, and another bus moves at 60, km/h in opposite directions.
    
    paragraph
    Relative velocity:
    $v_{AB}$ = 60 + 60 = 120 km/h
47. When solving collinear motion problems, consider the directions and use vector addition or subtraction.
48. Positive values indicate motion in the same direction as the reference frame.
49. Negative values indicate motion in the opposite direction.
50. Always include the correct units for velocity and ensure consistent conversions between km/h, m/s, etc.
    paragraph

Jamb(utme) key points on linear motion; speed; velocity; acceleration; equation of uniformly accelarated motion

Linear Motion

1. Linear motion occurs when an object moves along a straight path.
2. Displacement is the shortest distance between two points in a straight line, with direction.
3. Distance is a scalar quantity; displacement is a vector quantity.
4. Linear motion can be uniform (constant speed) or non-uniform (varying speed).
5. Linear motion is analyzed using kinematic equations under constant acceleration.
6. Examples include a car moving on a straight road or free-falling objects.
   paragraph

Speed

7. Speed is the rate of change of distance with respect to time.
8. SI unit of speed is meters per second m/s
9. Speed is a scalar quantity; it does not indicate direction.
10. Average speed is total distance divided by total time.
11. Instantaneous speed is the speed of an object at a specific instant.
12. The speed of light in a vacuum is the universal maximum speed limit.
    paragraph

Velocity

14. Velocity is the rate of change of displacement with respect to time.
15. Formula: $Velocity$ = $\frac{Displacement}{Time}$
16. SI unit of velocity is also m/s
17. Velocity is a vector quantity; it has both magnitude and direction.
18. Constant velocity implies zero acceleration.
19. Average velocity is the total displacement divided by total time.
20. Instantaneous velocity is the velocity of an object at a specific point in time.
21. Velocity can change due to a change in speed, direction, or both.
    paragraph

Acceleration

22. Acceleration is the rate of change of velocity with respect to time.
23. Formula: $Acceleration$ = $\frac{\Delta{Velocity}}{\Delta{Time}}$
24. SI unit of acceleration is ${m/s}^2$
25. Acceleration is a vector quantity.
26. Positive acceleration indicates an increase in velocity.
27. Negative acceleration (deceleration) indicates a decrease in velocity.
28. Uniform acceleration means constant acceleration over time.
29. Non-uniform acceleration means varying acceleration over time.
    paragraph

Equations of Uniformly Accelerated Motion

30. The three main kinematic equations describe uniformly accelerated motion:

• $v = u + at$,
• $s = ut$ + \frac12at^2 $
• $v^2 = u^2 + 2as$

31. $v$: Final velocity $(m/s)$
32. $u$: Initial velocity $(m/s)$
33. $a$: Acceleration $({m/s}^2)$
34. $t$: Time (s)
35. s: Displacement (m)
    paragraph

Deducing the Equations of Motion

36. First Equation: v = u + at

• Derived from the definition of acceleration: $a = \frac{v - u}{t}$ ⇒ v = u + at

37. Second Equation: $s = ut + \frac{1}{2}at^2$

• From the average velocity (Avg. velocity) = $\frac{u + v}{2}$ s = Avg. velocity $\times$ t, Substitute v = u + at into 's': $s = ut + \frac{1}{2}at^2$

38. Third Equation: $v^2 = u^2 + 2as$

• Derived by eliminating time (t) using: v = u + at and $s = ut + \frac{1}{2}at^2$
  paragraph

Practical Applications

39. Free-fall motion is an example of uniformly accelerated motion due to gravity.
40. Projectile motion combines horizontal and vertical linear motion.
41. Velocity-time graphs help visualize uniformly accelerated motion.
42. The slope of a velocity-time graph represents acceleration.
43. The area under a velocity-time graph represents displacement.
44. The slope of a distance-time graph represents speed.
45. Deceleration examples include braking a car or a ball rolling to a stop.
    paragraph

Key Points on Uniform Acceleration

46. Uniform acceleration simplifies calculations in physics.
47. It assumes external forces, like friction, are negligible.
48. Real-life motions, like a car accelerating on a highway, approximate uniform acceleration over short intervals.
49. Constant acceleration applies in cases like gravity near Earth's surface $9.8{m/s}^2$
50. Uniform acceleration equations are foundational in both physics and engineering.
    paragraph

Jamb(utme) key points on motion under gravity; distance time graph; velocity graph; instantaneous velocity; acceleration

Motion Under Gravity

1. Gravity causes all objects to accelerate toward Earth at $9.8{m/s}^2$ $( approximation: 10 {m/s}^2 )$
2. Free-fall motion is motion under the influence of gravity alone, with no air resistance.
3. Objects in free fall start with an initial velocity of zero if dropped from rest.
4. The equations of motion can be applied to free-fall scenarios, replacing acceleration $a$ with $g$
5. Upward motion against gravity is decelerated by $-g$, slowing the object.
6. At the highest point in upward motion, velocity is zero momentarily.
7. The time to rise to the highest point equals the time to fall back to the original height.
8. In free fall, heavier and lighter objects fall at the same rate without air resistance.
9. The displacement in free-fall motion can be calculated using $s = \frac{1}{2} g t^2$ for an object dropped from rest.
10. The velocity of a freely falling object after time $t$ is $v = g t$
11. For objects thrown upward, the time to reach the highest point is $t = \frac{u}{g}$, where $ u 4 is the initial velocity.
12. The total flight time for an object thrown upward is $T = \frac{2u}{g}$.
    paragraph

Distance-Time Graph

13. A distance-time graph shows how the distance of an object changes over time.
14. A straight line with a positive slope represents constant speed.
15. A horizontal line means the object is stationary (no movement).
16. A curved line indicates acceleration or deceleration.
17. A steeper slope on the graph represents a higher speed.
18. The slope of the graph is the speed of the object.
19. For free-fall motion, the graph is a curve that becomes steeper over time.
20. For uniformly accelerated motion, the distance-time graph is a parabola.
    paragraph

Velocity-Time Graph

21. A velocity-time graph shows how velocity changes with time.
22. A horizontal line indicates constant velocity (no acceleration).
23. A line with a positive slope indicates acceleration.
24. A line with a negative slope (sloping downward) indicates deceleration.
25. The area under the velocity-time graph gives the displacement.
26. A curved velocity-time graph represents non-uniform acceleration.
27. In free-fall motion, the velocity-time graph is a straight line starting from zero with a positive slope.
    paragraph

Instantaneous Velocity

28. Instantaneous velocity is the velocity of an object at a specific moment in time.
29. It can be found by calculating the slope of the tangent to the distance-time graph at a given point.
30. Instantaneous velocity is useful for analyzing non-uniform motion.
31. If velocity changes constantly, the instantaneous velocity equals the average velocity at the midpoint of the time interval.
    paragraph

Acceleration

32. Acceleration measures how quickly velocity changes with time.
33. Uniform acceleration means the velocity changes at a constant rate.
34. Non-uniform acceleration means the velocity changes at a varying rate.
35. Acceleration due to gravity, denoted $g$, is always $9.8 {m/s}^2$ downward near Earth's surface.
36. Deceleration is negative acceleration, reducing the velocity of an object.
37. In free-fall motion, acceleration remains constant regardless of direction (upward or downward).
    paragraph

Solving Problems of Motion Under Gravity

38. Identify the initial velocity $(u)$, final velocity $( v )$, acceleration $( a )$, displacement $( s )$, and time $(t)$,
39. Choose the correct kinematic equation based on the known and unknown quantities.
40. For objects dropped from rest, $u = 0$ and $a = g$.
41. Use $v = u + at$ to calculate the velocity at any time.
42. Use $s = ut + \frac{1}{2}at^2$ to find displacement after time $t$.
43. For objects thrown upward, remember that gravity acts downward, so $a = -g$.
44. To calculate the maximum height reached, use $v^2 = u^2 - 2g s$, setting $v = 0$.
    paragraph

Computing Instantaneous Velocity and Acceleration

45. For instantaneous velocity, find the slope of the tangent to a distance-time graph at a specific time.
46. For instantaneous acceleration, calculate the slope of the tangent to a velocity-time graph.
47. Use derivatives in calculus: $v = \frac{ds}{dt}$ for instantaneous velocity and $a = \frac{dv}{dt}$ for instantaneous acceleration.
48. In free-fall motion, instantaneous velocity at time $t$ is $v = gt$ if starting from rest.
49. Acceleration remains constant for uniformly accelerated motion, so $a = g$ throughout free fall.
50. For more complex cases, use graphs or calculus to compute values at specific moments.
    paragraph
    If you are a prospective Jambite and you think this post is resourceful enough, I enjoin you to express your view in the comment box below. I wish you success ahead. Remember to also give your feedback on how you think we can keep improving our articles and posts.
    paragraph

I recommend you check my article on the following: