Starting from rest, a boulder rolls down a hill with constant acceleration and travels 2.00m duering the first second.

Question

How far does it travel during the second second?
How fast is it moving at the end of the first second? At the end of the second second?

Answer 1

To solve this problem, we need to use the equations of motion for constant acceleration.

1. How far does it travel during the second second?
The formula we can use to solve this is:
distance = initial velocity * time + (1/2) * acceleration * time^2

Given:
initial velocity = 0 (as it starts from rest)
time = 2 seconds
acceleration = constant

Since the acceleration remains constant, we can use the formula:
distance = (1/2) * acceleration * time^2

Plugging in the values:
distance = (1/2) * acceleration * (2)^2
2m = 2 * acceleration

Therefore, the boulder travels 2 meters during the second second.

2. How fast is it moving at the end of the first second? At the end of the second second?
The formulas we can use to solve these are:
velocity = initial velocity + acceleration * time

Given:
initial velocity = 0 (as it starts from rest)
time = 1 second for the end of the first second
time = 2 seconds for the end of the second second
acceleration = constant

Plugging in the values for the first second:
velocity = 0 + acceleration * 1
velocity = acceleration

Therefore, at the end of the first second, the boulder is moving at a velocity equal to the acceleration.

Plugging in the values for the second second:
velocity = 0 + acceleration * 2
velocity = 2 * acceleration

Therefore, at the end of the second second, the boulder is moving at a velocity equal to twice the acceleration.