Consider a ball that picks up a speed of 3 m/s each second when its rolls from rest down an inclined plane. If the ball takes 4 seconds to reach the bottom, its speed at the bottom will be?
The acceleration rate is a = 3.0 m/s^2
After 4 seconds, its speed is a*4 = 12 m/s, if it started from reat.
To find the speed of the ball at the bottom of the inclined plane, we can calculate the cumulative speed gained during the 4 seconds.
Given:
Acceleration of the ball on the inclined plane = 3 m/s²
Time taken to reach the bottom = 4 seconds
We can use the equation of motion:
v = u + at
Where:
v = final velocity (speed)
u = initial velocity (speed)
a = acceleration
t = time
Given that the ball starts from rest (u = 0), we can substitute the values into the equation:
v = 0 + 3 m/s² × 4 s
Simplifying:
v = 12 m/s
Therefore, the speed of the ball at the bottom of the inclined plane will be 12 m/s.
To determine the speed of the ball at the bottom of the inclined plane, we need to consider the rate at which the ball is accelerating.
Given that the ball picks up a speed of 3 m/s each second, we can calculate the acceleration of the ball using the equation:
acceleration = change in speed / time taken
The change in speed can be calculated as the product of the acceleration and the time taken:
change in speed = acceleration * time taken
Substituting the known values, we have:
change in speed = 3 m/s/s * 4 s
change in speed = 12 m/s
Therefore, the speed of the ball at the bottom of the inclined plane is 12 m/s.