A 3 kg mass is attached to the end of a spring with spring constant 48 N/m. There is a damper which is tuned so that the damping is exactly critical. The mass is pulled 3 meters from rest position and let go (initial velocity is zero). Find the position of the mass as a function of time t: x = help (formulas) The mass will go towards the rest position, it will go past the rest position, and then it will slowly go back towards the rest position. At what time does it hit the rest position: seconds help (numbers) Book: Section 2.4 of Notes on Diffy Qs

You car is moving along in cruise control at a constant speed of 88.3 ft/s (about 60 mi/hr).  A text message appears on your phone and you look down to read it.  When you look back up at the road, you see a car at a complete stop in your lane 156 ft ahead of you.  It takes 0.39 s for you to react and apply the brakes.  When the brakes are applied your car experiences an acceleration of -32.3 ft/s2.  Fortunately, you are able to avoid hitting the other car.  What is the distance between the two cars when you come to a complete stop? (0.9 ft).

Suppose a rock falls from rest from a height of 100 meters and the only force acting on it is gravity. Find an equation for the velocity v(t) as a function of time, measured in meters per second. Hint What is the initial velocity of the rock?

Kim throws a ball against a wall at timet = 0. At time t = 1, it hits the wall and then at time t = 2 it is back where it started. If the average speed of the ball is 10 miles per hour, can you apply the MVT to show that the baseball must be traveling at 10 miles/hr at some point between [0,2]?

Car A is traveling at a constant speed v,=130 km/h at a location where the speed limit is 100 km/h. The police officer in car P observes this speed via radar. At the moment when A passes P, the police car begins to accelerate at the constant rate of 6 m/s' until a speed of 160 km/h is achleved, and that speed is then maintained. Determine the distance required for the police officer to overtake car A. Neglect any nonrectilinear motion of P. A P Ans. 713 m Repeat the previous problem, only now the driver of car A is traveling at va-130 km/h as it passes P, but over the next 5 seconds, the car uniformly decelerates to the speed limit of 100 km/h, and after that the speed limit is maintained. If the motion of the police car P remains as described In the previous problem, determine the distance required for the police officer to overtake car A. Ans. 330 m

Consider the following position function. Find ​(a) the velocity and the speed of the object and ​(b) the acceleration of the object.   r(t)=(4t^3,5t^2) for t≥0 (a)v(t)=? |v(t)=? ​(b) a(t)=?