Solve these problems:

1. At what times t, if any is a particle moving towards the

origin[x=0] if its position as a function of time is given by

a. x(t) = 2m cos(t/(2s))

b. x(t) =-(2 m/s²)t² - (2 m/s³)t³

2. A mouse is moving in a straight line. At 2 .0 m/s and is at position x=0 at time t=0, when it notices that a cat is behind it and begins to accelerate (still in the same direction) at 20 m/s² . What is the position of the mouse at time t=0.25 s?

3. A rock moves only in the vertical direction. Its acceleration is constant at -160 cm/s² , its initial velocity is 480 m/s and its initial height is 1400 mm.What is the greatest height the rock reaches?

When does it reach that height? What is its average velocity on the way up?

4. A bullet is shot with initial speed 300 m/s into a sandbag where it experiences an acceleration of 60.0 km/s in the direction to slow it down. How far does the bullet travel before coming to rest?

5. A 1X10⁵ g mass professor experiences a net force of 1.0X10⁸ g cm s^-2

directed straight downward and falls. He is at rest at height 20.00 m at time t exactly 0 seconds. Take the upward direction to be positive.

a. What is the magnitude of his acceleration in SI units?

b. At what height is he at time t=0.10 seconds?

c. What is his velocity when he is at height 19.80 m?

d. Suppose he had jumped so that at time t exactly 0 seconds his velocity was 2.0 m/s upward (but his height was the same as above).

What would be his height at time t=0.10 second.

6. A constant force acts on an object of mass 20 kg for 5.0 s, causing it to reach a velocity of 40 m/s i +30 m/s j having started from rest. Find the force, its magnitude and its direction.