What’s This Got To Do With Physics? Property of Texas Tech University Department of Mathematics & Statistics

Physics and Derivatives

Falling Body Formula

Example

Example

Example

Example

𝑣(1) = 90 + - + 3 6 8 𝑠𝑖𝑔𝑛 𝑜𝑓 𝑣(𝑡) [0, 3) ∪ (6,8]

+ - 3 6 8 𝑠𝑖𝑔𝑛 𝑜𝑓 𝑣(𝑡) (3, 6)

- + 4.5 8 𝑠𝑖𝑔𝑛 𝑜𝑓 𝑎(𝑡) Decelerating [0, 4.5) Accelerating (4.5, 8]

78 m t=8 s=240 t=6 s=162 t=3 s=202.5 t=0 s=0 40.5 m 202.5 m 202.5 + 40.5 + 78 = 321 𝑚

Graph of 𝑠(𝑡)

Simple Harmonic Motion Pendulum Block Attached To A Spring

Simple Harmonic Motion 3 -3 Block Attached To A Spring

Simple Harmonic Motion 3 -3 - + 1 2 𝑠𝑖𝑔𝑛 𝑜𝑓 𝑣(𝑡) Block Attached To A Spring

Simple Harmonic Motion 3 - + 1 2 𝑠𝑖𝑔𝑛 𝑜𝑓 𝑣(𝑡) -3 Block Attached To A Spring

Simple Harmonic Motion 3 - + - -3 1.5 2 0.5 𝑠𝑖𝑔𝑛 𝑜𝑓 𝑎(𝑡) Block Attached To A Spring

Simple Harmonic Motion 3 - + - 1.5 2 0.5 𝑠𝑖𝑔𝑛 𝑜𝑓 𝑎(𝑡) -3 Block Attached To A Spring

Simple Harmonic Motion 3 6 + 6 = 12 𝑐𝑚 6 cm -3 Block Attached To A Spring