1) 20 pts. The position of a particle is related to time by: X(t) = (At*- Bt + C)m where A = 8 m/s' , B = 6 m/s and C = 4 m a) Find the instantaneous velocity and acceleration as a function of time b) Find the velocity and acceleration of the particle after 10 seconds c) Is the particle accelerating of decelerating at 10 sec, why? d) Find the average velocity between 2 and 6 seconds e) Find the average acceleration between 2 and 6 seconds 2) 20 pts A person is running at his maximum velocity of 8 m/s to catch a train. When the person is 30 meters from the train, the train starts from rest with constant acceleration of 1 m/s". a) Can the person catch the train? b) If so, how far will he have to run when the train started to move? c) How fast is the train going when he catches it? 3) 20 pts. An airplane pilot pulls out of a dive by following an arc of a circle with constant radius 300 meters. At the bottom of the arc, the plane is going 180 km/hr. a) What is the magnitude and direction of the acceleration of the plane at this point? b) IF the plane maintains this are and starts to accelerate at 5 m/s when it is at the bottom of the arc, what is the magnitude of its acceleration after 3 seconds. I km/hr = 0.278 m/s 4) 20 pts. A large boulder rests on a cliff 400-meters above a small village is such a position that if it should roll off, it would leave the cliff with a speed of 50 m/s. There is a pond of diameter 200- meters situated with its edge 100-meters from the base of the cliff. The village is at the edge of the pond. a) Will the boulder hit the village? b) What is the velocity of the boulder when it hits? c) How long will the boulder be in the air? *Vo =som Hoom 190 200m 5) 20 pts. An airplane has an airspeed of 960 km/hr and its compass says it is flying 20 degrees north of west. There is a wind speed of 190 km/hr, 80 degrees south of west. Determine: a) The velocity (magnitude and direction) of the plane relative to the ground b) If the distance to the plane's destination is 1300 km, how long will the trip take?PHYSICS 105 EQUATION SHEET = AX g = 9.8 m/sec/sec At g = 32.2 ft/sec/sec a avg = AV At a fatal = a, + a, V = ddx a, = dv dt a = dy dt a= Vape = Ar v = Vo + at At (x - X,) = Vit +1/2at2 a avg = Av At v = Vo + 2a(x-X.) v+Vo 7= 2 dr dt ( x - Xo ) = VI a =