A rolling ball has an initial velocity of 1.6 m/s if the ball has a constant acceleration of .33 what is the velocity after 3.6 and the how far did the ball travel
Well, if the ball has a constant acceleration, it's safe to say it's on its way to becoming a famous athlete. Let's calculate its velocity after 3.6 units of time and find out how far it traveled.
To find the final velocity, we can use the formula:
vf = vi + at
Where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.
So, plugging in the values, we have:
vf = 1.6 m/s + (0.33 m/s^2)(3.6 s)
Calculating that, we get:
vf = 1.6 m/s + 1.188 m/s
vf ≈ 2.788 m/s
Great! Now we have the final velocity. Let's find out how far the ball traveled.
To find the distance traveled, we can use another handy formula:
d = vi * t + 0.5 * a * t^2
Where d is the distance traveled, vi is the initial velocity, a is the acceleration, and t is the time.
So, plugging in the values, we have:
d = (1.6 m/s)(3.6 s) + 0.5(0.33 m/s^2)(3.6 s)^2
Calculating that, we get:
d ≈ 5.76 m + 2.706 m
d ≈ 8.466 m
So, after 3.6 units of time, the velocity of the rolling ball is approximately 2.788 m/s, and it traveled approximately 8.466 meters. I hope this answers your question with a touch of laughter!
To solve this problem, we can use the equations of motion.
Step 1: Find the final velocity after 3.6 seconds.
Using the equation:
v = u + at
where
v = final velocity
u = initial velocity
a = acceleration
t = time
Given:
u = 1.6 m/s
a = 0.33 m/s^2
t = 3.6 s
Plugging the values into the equation, we have:
v = 1.6 + (0.33 × 3.6)
Calculating:
v = 1.6 + 1.188
Therefore, the velocity after 3.6 seconds is approximately 2.788 m/s.
Step 2: Find the distance traveled by the ball.
Using the equation:
s = ut + (1/2)at^2
where
s = distance
u = initial velocity
a = acceleration
t = time
Given:
u = 1.6 m/s
a = 0.33 m/s^2
t = 3.6 s
Plugging the values into the equation, we have:
s = (1.6 × 3.6) + (0.5 × 0.33 × (3.6)^2)
Calculating:
s ≈ 5.76 + 0.891
Therefore, the ball traveled approximately 6.651 meters.
To find the velocity after a given time and the distance traveled, we can use the basic equations of motion.
First, let's calculate the final velocity after 3.6 seconds:
Using the equation:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Substituting the given values:
u = 1.6 m/s
a = 0.33 m/s^2
t = 3.6 s
We can now calculate the final velocity:
v = 1.6 m/s + (0.33 m/s^2 * 3.6 s)
v = 1.6 m/s + 1.188 m/s
v = 2.788 m/s
Therefore, the velocity after 3.6 seconds is 2.788 m/s.
Now, let's find the distance traveled by the ball after 3.6 seconds:
Using the equation:
s = ut + (1/2)at^2
where:
s = distance
u = initial velocity
t = time
a = acceleration
Substituting the given values:
u = 1.6 m/s
a = 0.33 m/s^2
t = 3.6 s
We can now calculate the distance traveled:
s = (1.6 m/s * 3.6 s) + (0.5 * 0.33 m/s^2 * (3.6 s)^2)
s = 5.76 m + 0.7128 m
s ≈ 6.4728 m
Therefore, the ball traveled approximately 6.4728 meters after 3.6 seconds.