Question

A child blows a leaf from rest straight up in the air. The leaf has a constant upward acceleration of magnitude 1.0 m/s². How much time does it take the leaf to displace 1.0 m upwards? Round the answer to two significant digits.

a. 0.45 s
b. 0.64 s
c. 1.00 s
d. 1.41 s

Answer 1

The time it takes for the leaf to displace 1.0 m upwards is approximately 1.41 seconds.

Step-by-step explanation:

To find the time it takes for the leaf to displace 1.0 m upwards, we can use the kinematic equation:

Δy = v0t + (1/2)at2

In this case, the initial velocity (v0) is 0 m/s since the leaf starts from rest. The downward acceleration (a) is -1.0 m/s² due to gravity. We can rearrange the equation to solve for time (t):

t = √(2Δy/a)

Substituting the given values, we have t = √(2 * 1.0 m / -1.0 m/s²) = √2 s ≈ 1.41 s, which corresponds to option d.