1° 1. "A particle moving in the xy-plane has acceleration vector t, 1+t .for all t 2 0. The particle is at rest at time t = 0. a. Give the velocity vector of the particle at time t= 0. b. Give the velocity vector of the particle at time t = 3. c. How fast is the particle moving at time't = 3? . d. What is the total distance traveled by the particle in the time interval 0sts 3?

An airplane flies horizontally at a speed of 369 km/h and drops a crate that falls to the horizontal ground below. Neglect air resistance.  A. If the altitude of the plane was 628 m, then how far, horizontally in meters, did the crate move as it fell to the ground?  B. What was the speed of the crate, in m/s, just before it hit the ground?

6. A train is moving with a constant speed. The train moves 60 meters for every 1.5 seconds that elapses. a. Assume that we get 40 by dividing 60 by 1.5. What is the name that is commonly given to a quantity represented by this number 40? b. To denote the quantity completely, what additional information must be given besides the number 40? c. How would you interpret the number 40 in this instance? Your answer should mention distance and time. d. Use your interpretation (not algebra) to find the distance the train moves in 2.5 seconds.

A stone is thrown straight up from the edge of a roof, 650650 feet above the ground, at a speed of 1616 feet per second.A. Remembering that the acceleration due to gravity is −32ft/sec2−32ft/sec2, how high is the stone 55 seconds later?B. At what time does the stone hit the ground?C. What is the velocity of the stone when it hits the ground?

Two trains are 900.0 kilometers apart. One is in Portland. The other is in San Francisco. They both begin traveling toward each other at the same time. The Portland train travels with an average velocity of 80.0 km/hr South. The San Francisco train travels North with an average velocity of 65.0 km/hr North.a. At what time will the two trains meet?b. How far away will they be from Portland when they meet?

On the Apollo 14 mission to the moon, astronaut Buzz Aldrin hit a golf ball with a golf club improvised from a tool. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hit the ball with a speed of 29 m/sm/s at an angle 22 ∘∘ above the horizontal.   a. how long was the ball in flight in seconds? b. how far did it travel in meters? c. If there was no air resistance, how much farther would it travel in meters on the moon than on earth?

An astronaut lands on a newly discovered planet (that has a nice gravitational constant). He proceeds to jump out of the spacecraft and onto the planet's surface. His height above the ground (in feet) after t seconds is given by the function h (t) =-3t2 +12t +36. A. How high off the ground is the astronaut after 1 second? B. What is the astronaut's velocity after 1 second? Is he traveling up or down? C. How fast is the astronaut traveling when he lands on the planet? D. When will the astronaut be at his highest point in the jump? E. Is the astronaut speeding up or slowing down after 2 seconds? At what rate?

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/seconds

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.

A ball is thrown straight upward from a height of 3.2 m with a velocity of 13.0 m/s. a. What is the maximum height the ball reaches? b. How long does it take the ball to reach the maximum height? c. What is the total time the ball is in the air? d. With what velocity does the ball impact the surface?