Chapter 18: Kinematics

Question 1

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

Answer 1

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) )

Question 2

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

Answer 2

• 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)

Question 3

• 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)

Answer 3

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

Question 4

• State the units of acceleration
• Calculate average acceleration and instantaneous acceleration

Answer 4

• Units: m s⁻²
• Average acceleration
  = v(t₂)-v(t₁) / t₂- t₁
• Instantaneous acceleration
  a(t) = v’(t) = s”(t)

Question 5

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

Answer 5

• 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