comes from our This equation, which of of constant acceleration can be put in yet another form which does not depend so much Before going to examples lets show first that our three equations for the special case on when we started our clock or where we called x = 0. For example at t = t2 we have handy equations for the special case, will be very useful. v(t₂) = at₂ + v(0) or and at t₁ we have Subtracting the second from the first gives and subtracting, v(t₂) - v(t₁)= a (t₂-1₁) v(t₂) = a (t₂-t₁) +v(t₁). This really says the same thing as the original equation: The velocity at the end of a time interval is the velocity at the beginning plus the acceleration times the time interval. Doing the same thing for the second equation we have v(t₁) = at₁ +v(0). 1 x(t₂) = at +v(0)t₂ + x(0) x(t₁) = = (t₂) - (t₁) = at +v(0)t₁ + x(0) 1 2a. (t – tỉ) + n(0)(tz - t) Exercise: Go through the algebra to show that the above leads to 1 x(t₂) − x(t₁) = a · (t₂ − t₁)² + v(t₁)(t2 − t₁). HINT: You have to use v(t₁) = at₁ +v(0). (This equation also has the same interpretation as the original equation if one considers time intervals.) Exercise: Show that the third formula, relating the values of v², leads to v² (1₂) - v² (t₁) = 2a [x(t₂) - (t₁)]. 1

Let C be the region between the circles x² + y² = 1 and x² + y² = 4. Let 2 2 2 F(x, y) = (²3³-²3V², 30³² Compute the circulation across C. Flux = y³, x³ - 3x²

Solve for #3

Can you can explain the proof of "the equation of continuity", in an easy-to-understand manner? Attached images are the proof my professor gave. I really do not understand all the simple v's , capital v's and all? Can you kindly explain it in an easy-to-understand manner? Thank you!