A crate with mass 32.5 kg initially at rest on a warehouse...

A crate with mass $32.5 \mathrm{~kg}$ initially at rest on a warehouse floor is acted on by a net horizontal force of $14.0 \mathrm{~N}$. (a) What acceleration is produced? (b) How far does the crate travel in $10.0 \mathrm{~s} ?$ (c) What is its speed at the end of $10.0 \mathrm{~s} ?$

Key Concepts

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the product of its mass and its acceleration. This principle, expressed as F = ma, is fundamental in determining how an object moves when a force is applied, and it serves as the foundation for analyzing the motion of objects in physics.

Kinematics under Constant Acceleration

Kinematics under constant acceleration involves the set of equations that relate displacement, velocity, acceleration, and time. These equations, such as s = ut + ½at² for displacement and v = u + at for final velocity (where u is the initial velocity), provide the tools necessary to calculate how far an object moves and how fast it is traveling after being subjected to a constant acceleration over a period of time.

Transcript

00:01 Alright, so we have a crate on a warehouse for being acted on by a net horizontal force.

00:10 So that is going to look a little, something like this.

00:14 Crates on the ground, we know it's mass, and we know the magnitude of the force that is being applied.

00:22 I call that f.

00:26 So the mass of the crate is 32 .5 kilograms, and then the force that is being applied is 14 newtons.

00:41 Okay, so part a is asking us to find the acceleration that the crate experiences.

00:48 We're going to use a variation on f equals ma, but in order to solve for the acceleration, so we take 14, divide that through by 32.

00:58 To 0 .5 in order to get that the acceleration experienced is 0 .431 meters per square second.

01:12 In part b, they are asking us to find the displacement how far the create moves over after a time interval of 10 seconds, if that's how long this force was applied for.

01:28 And so the obvious kinematics equation to use is the one with the square involves.

01:35 And then one extra piece of information that's given to us is that the crate began from rest.

01:42 Okay.

01:44 So that means that this first term is going to go to zero.

01:48 And then we can just plug in numbers into the second term of this equation.

01:52 So we just solved the acceleration that was 0 .431.

01:57 Keep the one half.

01:58 And then the time interval is 10 seconds...