physics

speed

• Definition: Distance covered per unit time.
  Formula: s= d/t
  Unit: meters per second (m/s)

velocity

• Definition: Displacement covered per unit time (vector quantity).
  

• Formula: v = x/t

• where x is displacement.
  Unit: meters per second (m/s)

acceleration

• Definition: Rate of change of velocity.
  

• Formula: a = v-u/t

• where u = initial velocity, v = final velocity.
  

• Unit: meters per second squared (m/s')

important acceleration notes

• Negative acceleration means deceleration.

• Acceleration due to gravity (freefall): g = 9.8 m/s' (downward)

• No air resistance means freefall condition.

acceleration and distance additional formula

• Displacement with constant acceleration: d = 1/2²

• where d = distance, a = acceleration, t = time.

vector additional

• Arrange vectors head to tail.

• Resultant vector connects start of first to end of last.

resultant speed

• Use Pythagorean theorem:
  R = square A²+ B²

example questions

• Acceleration of a car braking to rest
  Given: initial velocity u = 15 m/s, final velocity v = 0, time t = 1.5 s.
  Find: acceleration a.
  Calculation:

a = v-u/t = 0-15/1.5 = 10 m/s²

• Calculate initial speed from stopping distance

Given: stopping time t = 2.5 s, stopping distance d = 5.0 m, final speed v = 0.

Find: initial velocity u

Using d = 1/2², and a = v-u/t solve for u. u = 2d/t - v = 2×5.0/2.5 - 0 =4.0 m/s

Vector addition with direction.

C = 3.1 North, D = 2.3 South

R = C - D

R = 3.1 - 2.3 = 0.8 m/s North

component of force

• Given: force F = 24 North at angle 0 = 50° to horizontal.
  Find horizontal component:
  horizontal = F x cos 0 = 24 x cos 50° = 15 N

airplane ground speed with wind

• Given: airplane speed 120 km/h East, wind speed 40 km/h West.
  Calculate ground speed:
  ground - V air + wind = 120 - 40 - 80 km/h East

deceleration of a car braking to rest

• Given: initial speed 4.0 m/s, final speed 0, time 1.2 s.
  Find acceleration:

a = s-u/t = 0-4.0/1.2 = -3.33 m/s²