# Newton's Second Law of Motion (problems)

• love_joyously
In summary, a 1.08 x 10^3 kg car uniformly accelerates for 12.0s from rest. During this time the car travels 132 m north. The net force acting on the car during this acceleration is 1.98 x 10^3 N north.
love_joyously
Hi I got a few questions that I could not answer about Newton's Second Law of Motion. Can someone please help me?

1) A 1.08 x 10^3 kg car uniformly accelerates for 12.0s from rest.. During this time the car travels 132 m north. What is the net force acting on the car during this acceleration?

2) A 1.20 x 10^3 kg car accelerates uniformly from 5.0m/s east to 12m/s east. During this acceleration the car travels 94m. What is the net force acting on the car during this acceleration?

I have no idea how my teacher got the answer 1.98 x 10^3 N north for Question 1 and 7.6 x 10^2 N east for question 2. Can anyone help me?

1) First $$F = ma$$, also you know the distance and time and that it started from rest, you can find the acceleration easily using $$d=\frac{at^2}{2}$$.

2) I am guessing you are having problems finding the acceleration. The acceleration is uniform here, so use $$d=\frac{v_1-v_0}{2}t$$ to find the time it takes to travel ($$v_0$$ and $$v_1$$ are the inital and final velocities respectively) and then using that time $$d=\frac{at^2}{2}+v_0t$$.

I hope this helps. Do not be discouraged when you cannot solve these, I almost failed physics my freshman year.

Last edited:
ok.. i got number 1 but I'm basically stuck on number 2. can u explain it clearly please?

In order to calculate the net force, you need the mass (given) and the acceleration. You will also indicate a direction of the force for this problem, as force is a vector quantity.

So, we all know $$F_{net} = ma$$

You have the mass, so let's solve for the acceleration.

Use one of those nice kinematic equations... I'll pick one.

$$v_{f}^2 = v_{i}^2 + 2ad$$

You know everything but "a", so use those algebra skills and solve for it.

The only difference between 1 and 2 is that in 1 the car starts from rest and in 2 it has initial speed 5 m/s.

With constant acceleration, a, from initial speed v0, an object will have speed v= v0+ at after time t and will have gone distance d= v0t+(1/2)at2. (You probably have those equations, or similar ones, in your textbook.)

In problem 2, you know the initial speed was 5 m/s and that the car went 94 m in 12 seconds: 94= 5(12)+ (1/2)a(12)2. Solve that for a and the use F= ma to find the force.

I would use the kinematic equation I gave because in the above way requires one to solve for time and then solve for acceration, when two steps aren't neccessary. It is quite correct though, and both ways will yield the same answer.

thank you! i got the answer now!

## 1. What is Newton's Second Law of Motion?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that the greater the force applied on an object, the greater its acceleration will be, and the greater the mass of the object, the lower its acceleration will be.

## 2. How do you calculate the acceleration of an object using Newton's Second Law?

The formula for calculating acceleration using Newton's Second Law is a = F/m, where a is the acceleration, F is the net force, and m is the mass of the object. This means that to calculate the acceleration, you need to divide the net force by the mass of the object.

## 3. Can you give an example of a problem involving Newton's Second Law?

Sure, let's say you have a cart with a mass of 10 kg and a net force of 20 N applied to it. Using the formula a = F/m, we can calculate the acceleration of the cart to be 20 N / 10 kg = 2 m/s².

## 4. How does Newton's Second Law relate to real-world situations?

Newton's Second Law is applicable to a wide range of real-world situations, from the motion of objects on Earth to the movement of planets in space. It helps us understand how forces affect the motion of objects and allows us to make predictions and solve problems in various scenarios.

## 5. What are some common misconceptions about Newton's Second Law?

One common misconception is that Newton's Second Law only applies to objects in motion. In reality, it also applies to objects at rest, as the acceleration of an object at rest is 0. Another misconception is that the net force and the acceleration have to be in the same direction, when in fact, they can be in different directions.

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