Tutorial Exercise The position function of a particle is given by r t t 4t t 16t When is the speed a minimum Step 1 To find when the speed is a minimum we need to find the speed as a function of t then find its derivative and see when it v t r t 2t 4 2t 16 2t 4 2t 16 Step 2 We remember that the speed is the magnitude of the velocity vector and is calculated as follows Iv t 2t 4 2t 16 V 8 Step 3 Next we use the Chain Rule to find the derivative of the speed v t 8 64t 272 1 2 8t 32 X 2 64 t 272 272