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A ball starts from rest. It rolls down a ramp and reaches the ground after 4 seconds. Its final velocity when it reaches the ground is 7.0 meters/second.
The initial velocity of the ball is ______ meters/second, and its acceleration is ______ meters/second².
To find the initial velocity and acceleration of the ball, we can use the equations of motion.
1. Initial Velocity (u): The ball starts from rest, so the initial velocity is:
[
u = 0 , text{meters/second}
]
2. Acceleration (a): We can use the formula for final velocity:
[
v = u + at
]
Where:
– ( v = 7.0 , text{m/s} ) (final velocity)
– ( u = 0 , text{m/s} ) (initial velocity)
– ( t = 4 , text{seconds} ) (time)
Plugging in the values, we get:
[
7.0 , text{m/s} = 0 + a cdot 4
]
Simplifying this:
[
7.0 = 4a
]
[
a = frac{7.0}{4} = 1.75 , text{meters/second}^2
]
So the answers are:
– Initial velocity: 0 meters/second
– Acceleration: 1.75 meters/second²
Feel free to ask if you have more questions!