Given that the acceleration vector is a(t)=(−1cos(−t),−1sin(−t),2t)a(t)=( −1cos⁡(−t),−1sin⁡(−t),2t), the initial velocity is v(0)=(1,0,1)v(0)=(1,0,1), and the initial position vector is r(0)=(1,1,1)r(0)=(1,1,1), Compute:a. The Velocity Vector v(t): _ i + _ j +_kb. The position vector r(t): _i + _ j + _k

Acave rescue team lifts an injured spelunker directly upward and out of a sinkhole by means of a motor-driven cable. the lift is performed in three stages, each requiring a vertical distance of 11.0 m: (a) the initially stationary spelunker is accelerated to a speed of 4.80 m/s; (b) he is then lifted at the constant speed of 4.80 m/s; (c) finally he is decelerated to zero speed. how much work is done on the 78.0 kg rescue by the force lifting him during each stage

You throw a small rock straight up from the edge of a highway bridge that crosses a river. the rock passes you on its way down, 7.00 s after it was thrown. what is the speed of the rock just before it reaches the water 28.0 m below the point where the rock left your hand? ignore air resistance.

Derive the formula 2as=v² -u² where the formula have have usual meanings