Answer:
Step-by-step explanation:
The net force acting on the ball is given by:
F_net = F_gravity - F_air
where F_gravity is the force due to gravity acting downwards and F_air is the force due to air resistance acting upwards.
F_gravity = m g, where m is the mass of the ball and g is the acceleration due to gravity.
F_air = b v, where b is a positive constant and v is the speed of the ball.
The acceleration of the ball is given by:
a = F_net / m
Substituting the expressions for F_gravity and F_air, we get:
a = (m g - b v) / m
Simplifying, we get:
a = g - (b/m) v
Therefore, the acceleration of the ball at any time is given by g - (b/m) v, where g is the acceleration due to gravity, b is a positive constant representing the air resistance force, m is the mass of the ball, and v is the speed of the ball. As the ball falls faster, the air resistance force increases, causing the acceleration to decrease.