A space vehicle starts at an initial velocity of 100 m/s along the positive x-axis, and accelerates into space. The acceleration is a(t)= (10m/s 3 )t 2 i + 2m/s 2 j The vehicle was at the origin at the time of the launch. Find the kinematic equations for the vehicle.  Vy(t) =

You are exploring a planet and drop a small rock from the edge of a cliff. In coordinates where the +y direction is downward and neglecting air resistance, the vertical displacement of an object released from rest is given by y − y0 = 1/2gplanett2, where gplanet is the acceleration due to gravity on the planet. You measure t in seconds for several values of y − y0 in meters and plot your data with t2 on the vertical axis and y − y0 on the horizontal axis. Your data is fit closely by a straight line that has slope 0.300 s2/m. Based on your data, what is the value of gplanet?

A cork bobs up and down in a lake. The distance from the bottom of the lake to the center of the cork at time t>=0 is given by s(t)= 25+cos(pi t), where s(t) is in feet and t Is in seconds. During what time interval is the cork rising. Draw pictures as well

Suppose that the position of a particle as a function of time is given by the expression: x(t) = (1t4 + 3t²) Î + 2t5ĵ Determine the velocity as a function of time, v(t) = Determine the acceleration as a function of time, a(t) = Determine the direction of the velocity at t = 1.4, 0v(t=1.4) = î + î+ degrees Ĵ Ĵ

An object is travelling in 1-dimension (i.e. along the x- axis) with a velocity described by the equation: v(t)=v0+1/6st^3 , where s and v0 are constants. The object’s position, and acceleration at time t = 0 are given by d0, and a0 respectively. In terms of the variables given, what is the average acceleration of the object over the interval from 0 to 2 seconds.

In a time of 2.67 h, a bird flies a distance of 86.7 km in a direction 30.2 degrees east of north. Take north to be the positive y direction and east to be the positive x direction. Express your answers in km/h. What is the x component of the bird’s average velocity?  What is the y component of the bird’s average velocity?

On a spacecraft two engines fire for a time of 389 s. One gives the craft an acceleration in the x direction of ax = 3.41 m/s^2, while the other produces an acceleration in the y direction of ay = 7.34 m/s^2. At the end of the firing period, the craft has velocity components of vx = 1860 m/s and vy = 4290 m/s. Find the (a) magnitude and (b) direction of the initial velocity. Express the direction as an angle with respect to the +x axis.

An object moves on xy plane according to the equation 7 = 20 cos(3t) î + (1,5t + 3,5t2)j. Determine its position at t = 0. Find its average velocity and average acceleration between t = 2s and t = 5s.

An unidentified flying object (UFO) is observed to travel a total distance of 49000 m, starting and ending at rest, over a duration of 3.07 s. Assuming the UFO accelerated at a constant rate to the midpoint of its journey and then decelerated at a constant rate the rest of the way, what was the magnitude of its acceleration? Express your answer in g s , where 1 g = 9.81 m/s^2.     20,796 g s     10,398 g s     2,120 g s     1,060 g s

A small object moves along the x-axis with acceleration ax(t) = −(0.0320m/s3)(15.0s−t). At t = 0 the object is at x = -14.0 m and has velocity v0x = 4.10 m/s. What is the x-coordinate of the object when t = 10.0 s?