The velocity of a particle is given by v = {16t²i + 4t³j + (5t +2)k}m/s, where t is in seconds. If the particle is at the origin when t=0, determine the magnitude of the particle's acceleration when t=2s. Also, what is the x, y, z coordinate position of the particle at this instant?

A particle starts from the origin at r=0 with a velocity of 8.0 m/s and moves in the xy plane with constant acceleration (3.5i +1.7)) m/s1. (a) When the particle's x coordinate is 27 m, what is its y coordinate? (b) When the particle's x coordinate is 27 r. what is its speed? m/s

The NEXT morning, you wake up in a strange room yet again, and this time you drop a ball from a height of 1.54 m above the floor. The ball hits the floor 0.392 s after your drop it. You guess that you must have been taken to an alien planet with gravity different from Earth s. What is this planet s g (that is, the magnitude of the acceleration due to gravity on this planet)?     10.0 m/s^2     15.0 m/s^2     30.0 m/s^2     20.0 m/s^2

I don't understand how to do this problem. I tried taking the derivative, but that didn't give me the correct answer. I would really appreciate the help. When a 1984 Alpha Romeo Spider sports car accelerates in the x-direction at the maximum possible rate,its motion during the first 20. seconds is extremely well modeled by the simple equation vx2=(60 m2/s3)t, where t is time in seconds and vx is in m/s. In other words, the squareof teh car's velocity increases linearly with time. What is its acceleration after 3s, assuming that the car starts from rest at t=0 s?

A remote-controlled car is moving around in a level (horizontal) parking lot. The velocity of the car as a function of time is given by: 3 = [5.0m/s – (0.018m/s³)t²]î + [2.0m/s + (0.55m/s²)t]j where î and ĵ are unit vectors representing two perpendicular directions on the horizontal ground (think of them as the East and North directions, if that helps you). b). What are the magnitude and direction of the car's velocity at t = 8.0 s? c). What are the magnitude and direction of the car's acceleration at t = 8.0 s? (Don't be intimated by the velocity function! Look at the î and ĵ components, and work each component separately to begin with, before combining components together to get any resultant vectors, if needed.)

The vector position of a particle varies in time according to the expression F(t)=(1.41 t + 1.72)i +(0.224t2 + 1.11)J where r is in meters and t is in seconds. Find the speed of the particle in m/s at 2.58 s.

A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by  x = 17.0t  and  y = 4.20t − 4.90t2,  where x and y are in meters and t is in seconds. (a) Write a vector expression for the ball's position as a function of time, using the unit vectors î and ĵ. (Give the answer in terms of t.) =          m By taking derivatives, do the following. (Give the answers in terms of t.) (b) obtain the expression for the velocity vector  as a function of time =          m/s(c) obtain the expression for the acceleration vector  as a function of time =          m/s2(d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 3.24 s.   =         m   =         m/s   =         m/s2

An object has an initial velocity of 29.0 m/s at 95.0° and an acceleration of 1.90 m/s2 at 200.0°. Assume that all angles are measured with respect to the positive x-axis. (a) Write the initial velocity vector and the acceleration vector in unit vector notation. (b) If the object maintains this acceleration for 12.0 seconds, determine the average velocity vector over the time interval. Express your answer in your unit vector notation.

A rocket's position (in meters) as a function of time (in seconds) is given below. Round all answers in this problem to one decimal place r² = (t² − 3t)i + (t³ + 3)ĵ (a) What is the magnitude of the rocket's (in m/s) velocity at t = 2.5 s? (b) In what direction is the rocket moving (in degrees) at t = 2.5 s? (c) What is the magnitude of the rocket's acceleration (in m/s²) at t = 2.5 s?

at an instant in time a particles velocity is v = (2.00i + 1.00j) m/s, while it’s acceleration is a = -1.00i m/s^2. at what rate is the particle speeding up / slowing down and what’s the radius of the curve on the particles trajectory