Chapter 18: Kinematics Flashcards

1
Q

Define:
- Kinematics
- Distance
- Speed
- Displacement
- Velocity
- Acceleration

A

Kinematics: study of motion

  • Distance: how far an object has travelled over time, regardless of direction of travel
  • Speed: how fast an object is travelling
    (Speed = Distance/Time)
  • Displacement, s(t): distance of an object relative to a fixed origin O
  • Velocity, v(t): rate of change of displacement
    (Average velocity = Change in distance/Change in time)
    (Velocity function v(t) = s’(t))
  • Acceleration, a(t) = Rate of change of velocity
    (Average acceleration = Change in velocity/Change in time)
    (Acceleration function a(t) = v’(t)= s”(t) )
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2
Q

Explain displacement in terms of using s(t) to determine the position of an object

A
  • When s(t) > 0, object is to the right of the origin O
  • When s(t) < 0, object is to the left of the origin O
  • Initial displacement: s(0)
  • Time object changes direction: turning point of s(t)
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3
Q
  • State the units of velocity
  • Calculate average velocity and instantaneous velocity
  • Use v(t) to determine travelling direction of object
  • Use velocity to find displacement
  • Find distance travelled from v(t)
A

Units: m s⁻¹

  • Average velocity = s(t₂)-s(t₁) / t₂- t₁
  • Instantaneous velocity = v(t) = s’(t)
  • When v’(t)>0, object is travelling to the right
  • When v’(t)<0, object is travelling to the left
  • When v’(t) = 0, object is at rest or is changing direction (if sign of v’(t) changes)
  • Displacement from velocity: integrate v(t) to find s(t)
  • Change in displacement
    = s(t₂)-s(t₁)
    = ∫ₜ₁ᵗ² v(t) dt [area under a velocity-time graph]
  • Total distance with a change in direction:
    ∫ₜ₁ᵗ² |v(t)|dt = ∫ₜ₁ᵗ² speed dt
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4
Q
  • State the units of acceleration
  • Calculate average acceleration and instantaneous acceleration
A
  • Units: m s⁻²
  • Average acceleration
    = v(t₂)-v(t₁) / t₂- t₁
  • Instantaneous acceleration
    a(t) = v’(t) = s”(t)
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5
Q

Distinguish between velocity and speed, and determine if speed is increasing or decreasing

A
  • Velocity: has size (magnitude) and sign (direction)
  • Speed: how fast an object is travelling, regardless of the direction
  • If the sign of v(t) and a(t) is the same, speed is increasing
  • If the sign of v(t) and a(t) is opposite, speed is decreasing
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