Chapter 2: Kinematics of Linear Motion

KOLEJ MATRIKULASI SELANGOR physics\akademik\1PN\SF016\ch2 2 Kinematics of Linear Motion 2.1 Linear Motion LINEAR MOTION – a movement in a straight line 1. Distance, d/ Unit: m – 2. Speed, v/ Unit: m s-1 – rate length of actual path of change of distance, v = ∆𝑑 between two points SUMMARY Graph s vs t v vs t a vs t Velocity = 0 ∆𝑡 3. Displacement, 𝑠⃗/ Unit: m – the distance between initial point and final point in a straight line 4. Velocity, 𝑣⃗/ Unit: m s-1 (i) Average velocity, vav – the rate of change of displacement, 𝑠2−𝑠1 ∆𝑠 vav = = 𝑡2−𝑡1 ∆𝑡 (ii) Instantaneous velocity, v – the instantaneous rate of change of displacement, 𝑑𝑠 v= 𝑑𝑡 (iii) Uniform velocity, 𝑑𝑠 = constant 𝑑𝑡 5. Acceleration, 𝑎⃗/ Unit: m s-2 (i) Average acceleration, aav – the rate of change of 𝑣2−𝑣1 ∆𝑣 velocity, aav = = 𝑡2−𝑡1 ∆𝑡 (ii) Instantaneous acceleration, a – the instantaneous rate of change of velocity 𝑑𝑣 𝑑2 𝑠 a= = 2 𝑑𝑡 𝑑𝑡 (iii) Deceleration – negative acceleration (object slowing down) (iv) Uniform acceleration, a= 𝑑𝑣 𝑑𝑡 = 𝑑2 𝑠 𝑑𝑡 2 = constant 6. (i) EXTRA: Negative Total distance traveled = velocity how far object moved = total path length = distanced moved Uniform (ii) Time taken = time elapsed velocity = time required = time interval Uniform (iii) Initial = original acceleration (iv) Uniform = constant = same (v) Increasing velocity = Uniform acceleration deceleration (vi) Decreasing velocity (slow down) = deceleration Velocity (vii) Zero velocity = the object increase is stationary (at rest) (viii) Negative velocity = the object moves in opposite Velocity direction decrease (ix) Uniform velocity = zero acceleration (x) Negative acceleration = 7. Graphical methods deceleration (retardation) (i) Displacement-time graph (ii) Velocity-time graph Gradient = Velocity Gradient = Horizontal line/ = Object is stationary/ Gradient = 0 not moving/ at rest Horizontal line/ = Gradient = 0 Non horizontal = Constant velocity/ straight line Acceleration = 0 Non horizontal = straight line Intersection on time- = Return to its original axis, t position Intersection on time- = axis, t Area under graph = 2.2 Uniformly accelerated motion 2.3 Free falling body - the vertical motion of a body at constant acceleration, g under gravitational field without air resistance Linear motion Free falling bodies v = u + at v = u – gt 1 1 s = ut + at2 s = ut – gt2 If object 2 2 moving with v2 = u2 + 2as v2 = u2 – 2gs At the highest constant Time to reach 1 point, vy = 0 𝑢 s = (u + v)t velocity, (a = H, t = 2 ms-1 𝑔 0), s = vt 𝑢2 H= (+)ve  acceleration (–)ve  deceleration Constant velocity Constant acceleration Object stops Distance travelled 2.4 Projectile motion 8. A projectile motion consists of two components: 8.1 horizontal component (x-comp.) - motion with constant velocity thus ax= 0 8.2 vertical component (y-comp.)- motion under constant acceleration, ay= g 9. The x-component of velocity along AC (horizontal) at any point is constant: ux = vx = u cos  10. The y-component (vertical) of velocity varies from one point to another point along AC, but the y-component of the initial velocity is given by: ux = vx = u sin  2𝑔 Velocity x-comp y-comp magnitude 11. The path followed by a projectil e is called trajector y Point P Point Q v1x = v2x = ux = u cos  (constant) v1y = uy – gt1 v2y = uy – gt2 2 2 v1 = √(𝑣1𝑥 )2 + (𝑣1𝑦 ) v2 = √(𝑣2𝑥 )2 + (𝑣2𝑦 ) Direction 1 = tan-1( 𝑣1𝑦 𝑣1𝑥 1 = tan-1( ) 𝑣2𝑦 𝑣2𝑥 ) 12. Formula Maximum height, H = 𝑢2 𝑠𝑖𝑛2  2𝑔 Time taken to reach maximum 𝑢 sin  height, t’ = Horizontal range, R = 𝑢2 𝑔 sin 2 Value of R maximum, Rmax =  = 45o 2𝑢 sin  Flight time, t (from point A to point C), t = 𝑢2 𝑔 , if 𝑔 𝑔 13. Horizontal projectile (i) Horizontal component along path AB. Velocity, ux = vx = u = constant Displacement, sx = x (ii) Vertical component along path AB. Initial velocity, uy = 0 m s-1 Displacement, sy = – h (iii) Formula Time taken for the ball to reach the floor 2ℎ (point B), t = √ 𝑔 2ℎ Horizontal displacement, x = u√ 𝑔