A particle moves accordingly to a law of motion s = f(t) = t^2 e^−t, t ≥ 0, where t is measured in seconds and s in feet. a. When is the particle speeding up? b. When is the particle slowing down?

B. Critical Thinking. Answer the following items.

A shot putter releases the shot some distance above the level ground with a velocity of 12.0 m/sm/s, 51.0∘∘ above the horizontal. The shot hits the ground 2.08 ss later. You can ignore air resistance 1. What is the x-component of the shot's acceleration while in flight? Express your answer in meters per second squared. 2.  What is the y-component of the shot's acceleration while in flight? Express your answer in meters per second squared.

3. The position of a drone as a function of time is given by m m *(t) = ( 8 i – 5 j+ 1.5 k) m + (-2 î + 4 j) t - t2j a. What is the x-position of the drone as a function of time? b. What is the y-position of the drone as a function of time? c. How far away is the drone from its starting position at t = 3s? What is the acceleration vector? e. What is the velocity vector as a function of time? f. At what time is the speed equal to 4 m/s?

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.

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?

a. Find the velocity v(t) and acceleration a(t). b. At what value of t does v=0? c. What is the maximum height?

If an object is dropped from a 196-foot-high building, its position (in feet above the ground) is given by s(t)= - 16t² + 196, where t is the time in seconds since it was dropped. a. What is its velocity 1 second after being dropped? b. When will it hit the ground? c. What is its velocity upon impact?

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by v⃗ =[ 5.00m/s − (0.0180m/s3) t2 ] i + [ 2.00m/s + (0.550m/s2) t ] j . a. What is the magnitude of the velocity of the car at t = 8.00 s? b. What is the direction (in degrees counterclockwise from + x-axis) of the velocity of the car at t = 8.00 s? c. What is the magnitude of the acceleration of the car at t = 8.00 s? d. What is the direction (in degrees counterclockwise from + x-axis) of the acceleration of the car at t = 8.00 s?

An airplane decelerates at a uniform rate of 8.0 m/s2 (a = -8.0 m/s2), until it stops after traveling 483 m. Determine: a. how fast was the plane traveling before it began to decelerate? b. Express your answer in scientific notation and in at least 3 significant figures.