A space shuttle is fired and the position of the shuttle is given by r(t)=(2*t*t-5*t)i+ (3*t+1)j+(12*t*t*t)k where t is in seconds, r is in meters and i.j,k are the unit vectors of x,y,z directions respectively. Find the average acceleration of the space shuttle between the time interval t=10s and t=1 minutes. * 5

The kinematic equations can describe phenomena other than motion through space and time. Suppose x represents a person's bank account balance. The units of x would be dollars ($) and velocity v would give the rate at which the balance changes (in units of, for example, $/month). Acceleration would give the rate at which v changes. Suppose a person begins with one thousand dollars in the bank. Initial money management leads to no net change in the account balance so that v. 0. Unfortunately, management worsens over time so that a = -2.42 x 102 $/month2. Assuming a is constant, find the amount of time in months until the bank account is empty. HINT months Mand Halan

The analytical method of adding vectors expressed in terms of their components may be applied to vectors in three dimensions, for which graphical work is inconvenient. Find the magnitude of the resultant of the vectors A = il2 - j37 + k58 and B = i5 + j30 - k42, where i, j, and k are unit vectors along the x, y, and z axes, respectively.

1d.  A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of  v0 = 18.5 m/s. The cliff is h = 20.0 m above a flat, horizontal beach as shown in the figure. Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.) x=  y=

The velocity vector of a sprinting cheetah has x- and y-components vx = +28.6 m/s and vy = −26.3 m/s. What is the magnitude of the velocity vector?

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 = 17.2t  and  y = 4.16t − 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 = 3.18 s.   =         m   =         m/s   =         m/s2

An object is dropped from rest and takes 2.42 seconds to reach the ground below. From what distance above the ground was it dropped? State this as a positive number and assume it has proper SI Units.

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.)

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.