3. A one dimensional problem. Assume v = v(t) = Determine the position and acceleration at time t = 3sec. 4t3 + 10t m/s. The initial position is r = 3 m.
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- 3. A jet plane has a takeoff speed of Vtakeoff = 60 m/s and can move along the runway at an average acceleration of 2.0 m/s². The runway is 1.5 km. a. Write out the 3 Kinetic equations. 2. v2-U2= Jas 3.5=uttata2 b. Write out the values of initial position, initial velocity, and acceleration. initial position uloity- a: 0.2m/s init.al aueleradion- How many seconds will it take for the plane to reach takeoff speed? С. d. How far will the plane have to travel to get to takeoff speed? e. will the plane be able to get to 60 m/s before it gets to the end of the runway?3. An object is dropped from a height h above the surface of the Earth such that it experiences an initial acceleration of 0.76g. Find the height h above the surface of the Earth. ME a = G (R, +h)Driving down the road at a speed of 23.9 m/s, you suddenly notice a fallen tree blocking the road a distance of 82.0 m ahead of you. You step on the brake pedal and decelerate at a constant rate. What must the magnitude of your acceleration be so that you will come to a stop 6.6 m in front of the tree? a. 3.79 m/s^2 b. 3.48 m/s^2 c. 3.22 m/s^2 d. 7.58 m/s^2
- 4. A robotic vehicle is exploring the surface of Mars. The robot, which is represented as a point, has x - and y-coordinates that vary with time: x = (3 − 2t); y = (-t² + 4t³) where x and y are in meters and t is in seconds. a. Find the average velocity of the robot between t = 0s and t = 2s. b. Find the average acceleration of the robot between t = 0s and t = 2s. c. At what time the acceleration of the robot will be zero. a. Vavg= -21 + 14ĵ m/s b. davg = 22ĵ C. m s² 2 t = = = 0.083 s 249: An archer fires an arrow straight up into the air with a speed v0=35.6m/s. Neglect air resistance. a. Find the maximum height, hℎ, in meters, reached by the arrow. b. In terms of known quantities, write an expression for the time the arrow is in the air until it returns to launch height.Include a picture or description of your coordinate system (origin, positive direction).
- 4. A car is driving at a speed of 25 m/s on a horizontal road. Determine the minimum distance in whichthe car will stop in each of the following cases.A. On a rainy day where µS = 0.125.B. On a sunny day where µS = 0.650.24. A rocket is fired upward on a straight upward trajectory at 90 degrees to the surface perfectly, starting from rest with an acceleration of +29.4 m/s² for the first 4 seconds of travel. After finishing these 4 seconds it runs out of gas but continues its upward movement on its original path for a short time. a. b. What is the maximum height it reaches? If after reaching the maximum height it is allowed to fall in free fall in a perfectly linear path towards the earth, what is its final speed just before hitting the ground? Select one: - b. a. Maximum height = 135.8 meters, final velocity = 940.8 meters/seconds Maximum height = 940.8 centimeters, final velocity = 135.8 centimeters/seconds c. Maximum height = 940.8 centimeters, final velocity = 13.58 meters/seconds d. Maximum height = 940.8 meters, final velocity = 135.8 meters/secondsa. Find the velocity v(t) and acceleration a(t). b. At what value of t does v=0? c. What is the maximum height?
- 2. A jet plane has a takeoff speed of vtakeoff = 73 m/s and can move along the runway at an average acceleration of 2.4 m/s2. The runway is 1.2 km. Write out the 3 Kinetic equations. a. b. Write out the values of initial position, initial velocity, and acceleration. How many seconds will it take for the plane to reach takeoff speed? с. d. How far will the plane have to travel to get to takeoff speed? will the plane be able to get to take off before it gets to the end of the runway? е.Given a particle that moves according to r(t) = (t2, t+,t-) t3 write the acceleration aa of the particle in the form a = aTT+aNN. at t = 0+ Select one: a. a(0) = 2T -N b. a(0) = 2N C. a(0) = 2T d. a(0) = T+N e. a(0) = N1. You are driving at 8.00 m/s south. You accelerate uniformly at 1.10 m/s? north for 5.00 seconds. How fast are you going at the end of the 5.00 seconds? What is your displacement?