Question

1. daniel is helping jane push boxes across the floor. daniel pushes a 50 kg box with a constant force of 150 newtons over 2 meters across a frictionless floor. how fast is the box moving after daniel finishes pushing the box?

Explanation:

Step1: Calculate the acceleration

According to Newton's second law \(F = ma\), where \(F = 150\space N\) and \(m=50\space kg\). Then \(a=\frac{F}{m}\).
Substitute the values: \(a=\frac{150}{50}=3\space m/s^{2}\).

Step2: Use the kinematic equation \(v^{2}=v_{0}^{2}+2ax\)

Since the box starts from rest, \(v_{0} = 0\space m/s\), \(a = 3\space m/s^{2}\), and \(x = 2\space m\).
The equation becomes \(v^{2}=0 + 2\times3\times2\).
Calculate \(v^{2}=12\).
Take the square - root of both sides: \(v=\sqrt{12}=2\sqrt{3}\approx 3.46\space m/s\).

Answer:

The box is moving at approximately \(3.46\space m/s\)