Final answer:
The final velocity of the marble is 6.0 m/s and the acceleration is 0.50 m/s². These values are calculated using the formulas for constant acceleration and the given data of the marble traveling 36 meters in 12.0 seconds from rest.
Step-by-step explanation:
The student's question asks about the final velocity and acceleration of a marble that accelerates from rest and travels a certain distance over a given time period. To find the final velocity (v) and acceleration (a), we can use the equations of motion for constant acceleration.
The formula for displacement (s) when starting from rest (initial velocity u = 0) is given by:
s = ut + ½ at²
Where:
- s is the displacement
- u is the initial velocity
- t is the time
- a is the acceleration
Since the initial velocity is zero (u = 0), the displacement formula simplifies to:
s = ½ at²
We can rearrange this to solve for acceleration (a):
a = 2s / t²
Using the given values of s = 36 m and t = 12.0 s, we can calculate the acceleration:
a = (2 × 36 m) / (12.0 s)² = 0.50 m/s²
Next, we can determine the final velocity using the formula:
v = u + at
Again, with the initial velocity being zero, the formula simplifies to:
v = at = 0.50 m/s² × 12.0 s = 6.0 m/s
Therefore, the final velocity of the marble is 6.0 m/s and the acceleration is 0.50 m/s².