A .250 kg ice puck starting from rest slides down a .80 m frictionless incline with a uniform acceleration of 6.5 m/s2. How long does it take the ice puck to reach the bottom of the ramp?
x = x initial + initial speed* t + (1/2) a t^2
here
0.80 = 0 + 0 + (1/2)(6.5) t^2
1.6/6.5 = t^2
t = sqrt (1.6 / 6.5)
not long
To find the time it takes for the ice puck to reach the bottom of the ramp, we can use the kinematic equation:
\[d = \frac{1}{2}at^2\]
Where:
d = distance (0.80 m in this case, since the puck slides down the incline)
a = acceleration (6.5 m/s²)
t = time (what we're trying to find)
Rearranging the equation to solve for t:
\[t = \sqrt{\frac{2d}{a}}\]
Plugging in the given values:
\[t = \sqrt{\frac{2 \times 0.80}{6.5}}\]
Simplifying:
\[t = \sqrt{\frac{1.6}{6.5}}\]
\[t = \sqrt{0.24615}\]
\[t \approx 0.496\] seconds
Therefore, it would take approximately 0.496 seconds for the ice puck to reach the bottom of the ramp.