Question

a student releases a marble from the top of a 80cm long ramp. the marble increases speed steadily and reaches the bottom of the ramp with a speed of 50cm/s. determine all unknowns and answer the following question.
si = 0 cm/s
s = 0 cm/s

Explanation:

Step1: Identify knowns and unknowns

We know the initial speed \( s_i = 0 \, \text{cm/s} \) (released from rest), final speed \( s_f = 50 \, \text{cm/s} \), and distance \( d = 80 \, \text{cm} \). We might be finding average speed or time. Let's first find average speed. The formula for average speed \( v_{avg} \) when acceleration is constant is \( v_{avg}=\frac{s_i + s_f}{2} \).
\( v_{avg}=\frac{0 + 50}{2}=25 \, \text{cm/s} \)

Step2: Find time taken

Using the formula \( d = v_{avg} \times t \), we can solve for time \( t \). Rearranging, \( t=\frac{d}{v_{avg}} \). Substituting \( d = 80 \, \text{cm} \) and \( v_{avg}=25 \, \text{cm/s} \), we get \( t=\frac{80}{25}=3.2 \, \text{s} \). Also, if we consider the final speed (maybe the question was about final speed, but \( s_f \) is given as 50 cm/s. Wait, the yellow box is \( s \) (maybe a typo, but likely final speed \( s_f = 50 \, \text{cm/s} \), so the unknown here (the yellow box) should be the final speed, which is 50 cm/s. Wait, the initial speed \( s_i = 0 \), final speed \( s_f = 50 \, \text{cm/s} \), distance \( d = 80 \, \text{cm} \). So the unknown in the yellow box (labeled \( s \)) is probably the final speed, which is 50 cm/s. Wait, maybe the problem is to fill the yellow box. Since the marble reaches the bottom with speed 50 cm/s, so \( s = 50 \, \text{cm/s} \).

Answer:

The value for \( s \) (final speed) is \( \boldsymbol{50} \, \text{cm/s} \)