Velocity
What are the rules of differentiation?
Let
𝑟⃗(𝑡) = 𝐴𝑡 𝑛 + 𝐵𝑡 𝑚 + 𝑐𝑡 + 𝐷
𝑣⃗(𝑡) =
𝑑𝑟⃗
= 𝐴(𝑛)𝑡 𝑛−1 + 𝐵(𝑚)𝑡 𝑚−1 + 𝑐
𝑑𝑡
Where A,B,C,D,n and m are constants
Examples 1
If the position function is:
𝑟⃗(𝑡) = 2𝑡 3 + 𝑡 2 + 4𝑡 + 5
Find the position and velocity at t = 2
Examples 2
If the position f
unction is:
𝑟⃗(𝑡) = 5
Find the position and velocity at t = 4
Examples 3
If the position function is:
𝑟⃗(𝑡) = −10𝑡 + 21
Find the position and velocity at t = 2
Examples 4
If the position function is:
𝑟⃗(𝑡) = 𝑡 7 + 5𝑡 4 + 2𝑡 + 1
Find the position and velocity at t = 1
Examples 5 (Advanced level)
If the position function is:
𝑟⃗(𝑡) = √𝑡
Find the position and velocity at t = 4