Physics Chapter 5

Position-Time Graph  Time is always on the x axis  The slope is speed or velocity Time (s) Position (m) Slope = Δ y Δ x

Velocity-Time Graph  Time is always on the x axis  The slope is acceleration  Area under the curve is position Slope = Δ y Δ x time (s) Velocity (m/s)

Area under velocity time graph is position Time (s) Velocity (m/s) Area = ½ b * h For this triangle A = ½ (velocity) (time)

Acceleration -Time Graph  Time is always on the x axis  Area under the curve is velocity time (s) Acceleration (m/s/s) Slope = Δ y Δ x

Area under acceleration time graph is velocity Time (s) Acceleration (m/s/s) Area = ½ b * h For this triangle A = ½ (acceleration) (time)

Acceleration is often graphed like this time (s) Acceleration (m/s/s) l+

Which makes area under the curve … time (s) Acceleration (m/s/s) l+ Area = b * h For this A = (acc) (time)

Looking at graphs  Average uses slope of the chord  Instantaneous uses slope of the tangent  If slope of the chord = slope of the tangent line then average = instantaneous

Average Velocity Which leads to a Kinematic Equation

Let time at 0 be 0 or

Position with Constant Velocity

Average acceleration Which leads to another Kinematic Equation

or Let time at 0 be 0

Final position with Constant acceleration

Time (s) Velocity (m/s) d = v 0 * t v0v0v0v0 v t d = ½ (v – v 0 ) * t or d = ½ vt – ½v 0 t Add them together & you get If the initial position is not zero, then add d 0 to the total distance

Final position with Constant acceleration

If v is not known, substitute the following equation in for v This leads to…

Final velocity with Constant acceleration Or simply

Final velocity with Constant acceleration Or simply

To solve this equation, note that it does not include time. Solve for t Sub t into:

Kinematic Equations