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) )
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)
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
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)
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