a ball is released from rest and rolls down in an inclined plane, requiring 4 sec. to cover a certain distance of 100m. a) what is the acceleration?
b) how many cm would it have fallen vertically in the same time?
a) a=2(distance)/time^2
= 2(100cm)/16s^2
=12.5 cm/s^2
b) s= (gt^2)/2
since g = 9.8 m/s^2
= (9.8 x 16)/2
=78.4 m
or 7840 cm
awesome
We will be glad to critique your thinking, but don't have time to do all your work for you. The average speed (25 m/s in this case) tells you that the final velocity 50 m/s. Divide that by the elapsed time for the aceleration.
I am sure you know the formula for the time to fall Y vertically.
Y = (1/2)g t^2
Use it. You may have to convert meters to cm.
a) Well, I don't know about you, but whenever I see a ball rolling down an inclined plane, I imagine it wearing little roller skates. It's quite a sight! Anyway, to find the acceleration, we can use the formula:
acceleration = (2 * distance) / (time^2)
Plugging in the values, we get:
acceleration = (2 * 100m) / (4s)^2
calculating... calculating... *drumroll please*
The acceleration is approximately 6.25 m/s². Just make sure the ball doesn't get any speeding tickets!
b) Ah, the good old vertical fall. The ball may not be a skydiver, but we can still calculate how many centimeters it would have fallen vertically in the same time.
Using the formula for vertical fall distance, which is:
distance = (1/2) * acceleration * (time^2)
We can plug in the values we know:
distance = (1/2) * 9.8 m/s² * (4s)^2
Calculating... calculating... *cue clown music*
The ball would have fallen approximately 78.4 cm vertically during its roller coaster ride down the inclined plane. That's quite a fall for a little ball, don't you think?
To find the acceleration of the ball rolling down the inclined plane, we can use the formula:
acceleration = change in velocity / time taken
Let's start by finding the change in velocity. The ball started from rest, so its initial velocity (u) is 0 m/s. The final velocity (v) can be calculated using the equation:
v = u + at,
where "a" is the acceleration and "t" is the time taken. Rearranging the equation, we have:
v = at.
Given that the time taken is 4 seconds, and the distance covered is 100m, we can rearrange the formula for distance covered:
distance = ut + (1/2)at^2.
Since the initial velocity is 0, the equation simplifies to:
distance = (1/2)at^2.
Plugging in the known values, we have:
100 = (1/2)a * (4^2),
100 = 8a.
Now, we can solve for the acceleration (a):
a = 100 / 8,
a = 12.5 m/s^2.
So, the acceleration of the ball rolling down the inclined plane is 12.5 m/s^2.
For part b), we need to find the vertical distance the ball would have fallen in the same time (4 seconds).
The vertical distance covered is given by the formula:
vertical distance = (1/2) * g * t^2,
where "g" is the acceleration due to gravity and "t" is the time taken.
Substituting the values, we have:
vertical distance = (1/2) * 9.8 m/s^2 * (4^2),
vertical distance = 9.8 * 16,
vertical distance = 156.8 m.
Therefore, the ball would fall vertically approximately 156.8 meters in the same time of 4 seconds.