Given that the acceleration vector is a(t) = ( -cos(t) )i - ( sin(t) )j + (2t)k, the
initial velocity is v(0) = i + k,
and the initial position vector is r(0) = i + j + k, compute:

A. The velocity vector v(t) = i + j + k

B. The position vector r(t) = i + j + k

v(t) = (-sin(t) + 1)i + (cos(t ) - 1)j + k

r(t) = (cos( t ) + t)i + (sin( t ) -t + 1)j + ()k

The work

4.

The position function of a particle is given by
.
At what time is the speed minimum?

-0.5

The work

5.

A dense particle with mass 7 kg follows the path
with units in meters and seconds.
What force acts on the mass at t = 0?

(, , ) kg*m/s^2

( 0, -448, 0) kg*m/s^2

The work

6.

A projectile is fired from ground level with an initial speed of 550
m/sec and an angle of elevation of 30 degrees. Use that the acceleration
due to gravity is 9.8 .
The range of the projectile is meters.
The maximum height of the projectile is meters.
The speed with which the projectile hits the ground is m/sec.

Range of projectile = 26731.91 meters.
Max height of projectile = 3858.42 meters.
Speed projectile hits ground = 550 m/sec.

The work

7.

A ball is thrown at an angle of 45 degrees to the ground, and lands
40 meters away.
The initial speed of the ball was m/sec.

19.799 m/sec

The work

8.

A body of mass 10 kg moves in a (counterclockwise) circular path of radius 8
meters, making one revolution every 12 seconds. You may assume
the circle is in the xy-plane, and so you may ignore
the third component.
A.
Compute the centripetal force acting on the body.
(,)
B.
Compute the magnitude of that force.