Forces and Laws of Motion Problem

[._|evo|_.]

Homework Statement

A car with a mass of 1100 kg is being pulled by a tow truck exerts a 500 N force on the car and there is a 300 N friction force acting on the car.

If the car starts at rest at time t=0, at what time has the truck moved 100 meters?

Homework Equations

x=v₀t + 1/2 at²

The Attempt at a Solution

First off, I attempted to draw a free body diagram.

Down is gravity
Up is normal force
left is friction force
right is the force acting on the car and the truck

Then I proceeded to fill in the variables for the equation above ^^^^
V₀ = 0
a = 0.20 m/s²
t=? (trying to figure this out)
x = 100

I ended up with this result: 31.62 seconds.

The teacher said it was 33 seconds.

Help would be appreciated.

 

[collinsmark]

Hello, "._|evo|_." (??!)

Then I proceeded to fill in the variables for the equation above ^^^^
V₀ = 0
a = 0.20 m/s²
t=? (trying to figure this out)
x = 100

Double check the
"a = 0.20 m/s²."
I don't think that's right. Take care of significant figures.

(Hint: Newton's second law directly applies here. Just make sure the significant figures are appropriate.)

 

[._|evo|_.]

What is the net force in this case?

 

[collinsmark]

What is the net force in this case?

One way to state Newton's second law is (this version of the Newton's second law assumes the mass is constant):

ma = Σ F

What that means is that the particular object's mass, times that object's acceleration, is the sum of all forces acting on that particular object.

It's important that when you sum together the forces, you treat them as vectors. A vector has a magnitude and direction. And they need to be added together with that in mind.

Whenever you have such a problem with multiple forces draw of free body diagram. Draw the forces as arrows, and make sure the point in the appropriate direction. Drawing a free body diagram is important, and I suggest getting into the habit of doing it. It will make things much easier.

So what forces are acting upon car in your problem? There is the force from the tow truck that has a magnitude of 500 N. There is also the force of friction that has a magnitude of 300 N.

Now take a look at your free body diagram. The two forces acting on the car are in opposite directions. So if we define the positive direction as being the direction toward the tow truck, the force on the car from the tow truck is +500 N. The force of friction is in the opposite direction, so the frictional force is -300 N (the minus sign means the friction force vector points in the "negative" direction as we have defined the directions). (This becomes obvious after you draw your free body diagram. So if you haven't drawn it yet, draw it now! )

Add the two forces together together. You know the mass is 1100 kg. Solve for a.

Once you know that, use the relevant equation you gave in your original post, and solve for t.