A car jumps off a ramp with a Kinetic energy of 5,000 joules. This same car has a gravitational potential energy of 4,685 joules at some point when it is falling to the ground, after jumping off the ramp. When the car lands on the ground, the springs of this car’s suspension compress and then come back to normal exerting an elastic potential energy of 4,968 joules. What is the car’s total mechanical energy (TME)?

Aparticle's position is given by x = 3.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) what is its velocity at t = 1 s? (b) is it moving in the positive or negative direction of x just then? (c) what is its speed just then? (d) is the speed increasing or decreasing just then? (try answering the next two questions without further calculation.) (e) is there ever an instant when the velocity is zero? if so, give the time t; if not, answer "0". (f) is there a time after t = 3 s when the particle is moving in the negative direction of x? if so, give the time t; if not, answer "0".