A soccer ball is released from the top of a smooth incline. After 3.80 s the ball travels 9.1 m. One second later it has reached the bottom of the incline. Assume the ball's acceleration is constant and determine its value ( m/s2)
ditance=1/2at^2. solve for a given t=3.8 d=9.1
1.26 m/s^2
To determine the acceleration of the soccer ball, we can use the kinematic equation:
\(s = ut + \frac{1}{2} a t^2\)
where:
s = distance traveled (9.1 m),
u = initial velocity (0 m/s, since the ball is released from rest),
t = time (3.80 s),
a = acceleration (unknown).
Plugging in the values, we get:
\(9.1 = 0 \times 3.8 + \frac{1}{2} a \times (3.8^2)\)
Simplifying the equation:
\(9.1 = \frac{1}{2} \times a \times 14.44\)
\(18.2 = a \times 14.44\)
To find the acceleration a, divide both sides of the equation by 14.44:
\(a = \frac{18.2}{14.44}\)
\(a \approx 1.26 \, \text{m/s}^2\)
Therefore, the value of the ball's acceleration is approximately 1.26 m/s².
To determine the acceleration of the soccer ball, we can use the kinematic equation:
\[s = ut + \frac{1}{2}at^2\]
Where:
- s is the distance travelled by the soccer ball
- u is the initial velocity of the soccer ball (which we assume to be zero since it is released from rest)
- a is the acceleration of the soccer ball
- t is the time elapsed
From the given information, we know that after 3.80 seconds, the ball travels a distance of 9.1 meters. Plugging these values into the equation, we have:
\[9.1 = 0 \cdot 3.80 + \frac{1}{2}a(3.80)^2\]
Simplifying the equation gives:
\[9.1 = 7.22a\]
Now, we need to find the time it takes for the ball to reach the bottom of the incline. From the given information, we know that it takes one more second after 3.80 seconds. Therefore, the total time elapsed is 3.80 seconds + 1.00 second = 4.80 seconds.
Using the same equation, we can now calculate the distance traveled by the ball at 4.80 seconds. Plugging in the values, we have:
\[s = ut + \frac{1}{2}at^2\]
\[s = 0 \cdot 4.80 + \frac{1}{2}a(4.80)^2\]
\[s = 11.52a\]
Since the distance traveled at 4.80 seconds is the entire incline, which we assume to be the same as the initial distance of 9.1 meters, we can equate the two distances:
\[9.1 = 11.52a\]
Now, we have two equations with two unknowns. We can solve this system of equations to find the values of 'a'.
Dividing the first equation by 7.22 gives:
\[1.26 = a\]
Substituting this value into the second equation gives:
\[9.1 = 11.52 \cdot 1.26\]
Solving for the value of 'a', we have
\[9.1 = 14.5152\]
Therefore, the acceleration of the soccer ball is approximately 1.26 m/s^2.