What is the restoring force of a spring with a spring constant of a 4a and a stretched displacement of 3b?

Jason and mia are both running in a race. as they approach the finish line, you being the physicist that you are decide to time how long it takes them to reach the end of the race. when you start your stop watch (you can take this as time t = 0 s) you notice that mia is an unknown distance d ahead of jason and both are moving with the same initial velocity v_0. you also notice that jason is accelerating at a constant rate of a_j, while mia is deaccelerating at a constant rate of -a_m. jason and mia meet each other for the first time at time t = t_1. at this time (t = t_1) jason's velocity is two times that of mia's velocity, meaning v_j (t_1) = 2v_m (t_1). a) draw the position vs. time graph describing mia's and jason's motion from time t = 0 to time t = t_1. clearly label your axes and initial conditions on your graph. b) draw the velocity vs. time graph describing mia and jason's motion from time t = 0s to time t = t_1. clearly label your axes and initial conditions on your graph. c) how long from when the stop watch was started at t = 0s did it take mia and jason to meet? express your answer in terms of know quantities v_0, a_m, and a_j. d) when the stop watch started at time t = 0s, how far apart, d, were mia and jason? express your answer in terms of know quantities v_0, a_m, and a_j.

After a big snowfall, you take your favorite rocket-powered sled out to a wide field. the field is 195 m across, and you know that your sled accelerates at a rate of 3.65 m/s2 when the rocket is on. how much time will it take the sled to cross the field starting from rest, assuming the rocket is on the whole time?

The rigid beam is supported by the three suspender bars. bars ab and ef are made of aluminum and bar cd is made of steel. if each bar has a cross-sectional area of 450 mm2, determine the maximum value of p if the allowable stress is (σallow)st = 200 mpa for the steel and ( σallow)al = 150 mpa for the aluminum. est = 200 gpa and eal = 70 gpa.