A mechanic pushes a 3540 kg car from rest to a speed of v, doing 4864 J of work in the process. Find the speed v. Neglect friction between car and road. Answer in units of m/s.

The image shows the positions of a car on a roller coaster track. arrange the cars in order based on their gravitational potential energy. begin with the lowest potential energy and end with the highest.

Visualize the problem and identify special cases first examine the problem by drawing a picture and visualizing the motion. apply newton's 2nd law, ∑f⃗ =ma⃗ , to each body in your mind. don't worry about which quantities are given. think about the forces on each body: how are these consistent with the direction of the acceleration for that body? can you think of any special cases that you can solve quickly now and use to test your understanding later? one special case in this problem is if m2=0, in which case block 1 would simply fall freely under the acceleration of gravity: a⃗ 1=−gj^.

Conventional hot-water heaters consist of a tank of water maintained at a fixed temperature. the hot water is to be used when needed. the drawback is that energy is wasted because the tank loses heat when it is not in use, and you can run out of hot water if you use too much. some utility companies are encouraging the use of on-demand water heaters (also known as flash heaters), which consist of heating units to heat the water as you use it. no water tank is involved, so no heat is wasted. a typical household shower flow rate is 2.50 gal/min (9.46 l/min ) with the tap water being heated from 51.0 ˚f (10.6 ˚c) to 120 ˚f (48.9 ˚c) by the on-demand heater.what rate of heat input (either electrical of from gas) is required to operate such a unit, assuming that all the heat goes into the water?