| Quantity | Variable a(t) | Constant a | |----------|---------------|-------------| | v(t) | ∫ a dt + C | v₀ + a t | | s(t) | ∫ v dt + C | s₀ + v₀ t + ½ a t² | | v² relationship | Not directly | v² = v₀² + 2a(s-s₀) |
Pay close attention to phrases like "starts from rest" ( ) or "passes origin" ( Integration Constants: Never forget +Cpositive cap C during indefinite integration. rectilinear motion problems and solutions mathalino upd
The negative sign indicates the displacement is from the bridge, which is the bridge's height above the water. | Quantity | Variable a(t) | Constant a
: "A stone is dropped from a captive balloon at an elevation of 1000 ft. Two seconds later another stone is thrown vertically upward from the ground with a velocity of 248 ft/s. When and where do the stones pass each other?" Solution Approach : Two seconds later another stone is thrown vertically