A ball rolls down a hill with a constant acceleration of 2.0 m/s2. If the ball starts from rest, (a) what is its velocity and the end of 4.0 s? (b) How far did the ball move?
8m/s
To find the velocity of the ball at the end of 4.0 seconds, we can use the kinematic equation:
v = u + a*t
where v is the final velocity, u is the initial velocity (which is zero in this case since the ball starts from rest), a is the acceleration, and t is the time.
(a) Substituting the given values into the equation, we have:
v = 0 + (2.0 m/s^2) * 4.0 s
v = 8.0 m/s
Therefore, the velocity of the ball at the end of 4.0 seconds is 8.0 m/s.
To find the distance the ball moved, we can use another kinematic equation:
s = u*t + (1/2)*a*t^2
where s is the distance, u is the initial velocity (again, zero in this case), a is the acceleration, and t is the time.
(b) Substituting the given values into the equation, we have:
s = 0 + (1/2)*(2.0 m/s^2)*(4.0 s)^2
s = 0 + (1/2)*(2.0 m/s^2)*(16 s^2)
s = 0 + 16 m
Therefore, the ball moved a distance of 16 meters.
To find the answers to these questions, we can use the equations of motion, specifically the equations for uniformly accelerated motion. Here's how:
(a) To find the velocity of the ball at the end of 4.0 s, we can use the equation:
v = u + at
Where:
v is the final velocity,
u is the initial velocity (which is 0 in this case, as the ball starts from rest),
a is the acceleration (given as 2.0 m/s²), and
t is the time taken (4.0 s).
Plugging in the values, we get:
v = 0 + 2.0 * 4.0
v = 8.0 m/s
So, the velocity of the ball at the end of 4.0 s is 8.0 m/s.
(b) To find how far the ball moved, we can use the equation:
s = ut + (1/2)at²
Where:
s is the distance traveled,
u is the initial velocity (again, 0 m/s),
a is the acceleration (2.0 m/s²), and
t is the time taken (4.0 s).
Substituting the values, we get:
s = 0 * 4.0 + (1/2) * 2.0 * (4.0)²
s = 0 + 0.5 * 2.0 * 16.0
s = 0 + 1.0 * 16.0
s = 16.0 m
So, the ball traveled a distance of 16.0 meters.
Therefore, the velocity of the ball at the end of 4.0 s is 8.0 m/s and the distance it moved is 16.0 meters.
a) 8/ms
b) 16m (Down)