Because the force of gravity attracts the comets towards the sun
1) The velocity of the particle is given by the derivative of the position. So, if we derive s(t), we get the velocity of the particle as a function of the time:

2) The acceleration of the particle is given by the derivative of the velocity. So, if we derive v(t), we get the acceleration of the particle as a function of the time:

Answer:
Part a)
v = 16.52 m/s
Part b)
v = 7.47 m/s
Explanation:
Part a)
(a) when the large-mass object is the one moving initially
So here we can use momentum conservation as the net force on the system of two masses will be zero
so here we can say

since this is a perfect inelastic collision so after collision both balls will move together with same speed
so here we can say



Part b)
(b) when the small-mass object is the one moving initially
here also we can use momentum conservation as the net force on the system of two masses will be zero
so here we can say

Again this is a perfect inelastic collision so after collision both balls will move together with same speed
so here we can say



The net force performs a total amount of work equal to
(45 N) (0.80 m) = 36 J
on the bullet, and this is in turn is equal to the change in the bullet's kinetic energy by the work-energy theorem. So we have
W = ∆K = 1/2 mv²
since the bullet starts at rest, where m = its mass and v = its final velocity.
Solve for v :
36 J = 1/2 (0.0050 kg) v² ⇒ v = 120 m/s