Calculating Distance Traveled by a Car Using Newton's Laws of Motion

This article delves into the physics behind calculating the distance a car travels under the influence of a given force, starting from rest. We will use Newton's Second Law of Motion and kinematic equations to model the car's motion accurately.

Understanding the Problem

You've been presented with a scenario where a 1500 kg car is subjected to a total horizontal force of 980 N. The question is: how far will the car travel?

Using Newton's Second Law of Motion

Newton's Second Law of Motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:

(F m cdot a)

Given:

(F 980 , text{N}) (m 1500 , text{kg})

Solving for Acceleration

First, we rearrange the equation to solve for acceleration:

(a frac{F}{m} frac{980 , text{N}}{1500 , text{kg}})

Calculating this, we get:

(a 0.6533 , text{m/s}^2)

Using Kinematic Equations to Find Distance

When starting from rest, the initial velocity (v_i 0). The kinematic equation for distance traveled is:

(d v_i t frac{1}{2} a t^2)

Since (v_i 0), the equation simplifies to:

(d frac{1}{2} a t^2)

Providing a Time Interval

You provided a distance of 8.16 meters but forgot to mention the time interval. Without an exact time duration, we cannot verify the distance. However, let's work through the example you provided:

You claimed a distance of 8.16 meters, and through rearranging the kinematic equation:

(8.16 frac{1}{2} cdot 1.531 cdot t^2)

Solving for (t):

(t 3.27 , text{seconds})

Therefore, if the time interval is 3.27 seconds, the car would indeed travel 8.16 meters under the given conditions.

Discussion on Incorrect Problem Statement

Interestingly, the scenario you described implies that the car is accelerating under the influence of a constant horizontal force. In such a situation, the car would continue to accelerate as long as the force remains constant, and thus, it is not appropriate to state that the car starts from rest and stops after covering a certain distance without mentioning the time interval.

It is possible that the question or the problem statement may have been incorrectly worded. It is essential for the problem statement to clearly indicate the time duration over which the force is applied to obtain the correct distance.

Conclusion

In conclusion, to accurately calculate the distance a car travels under the influence of a horizontal force, it is crucial to know the time duration over which the force is applied. Using Newton's Second Law and kinematic equations, we can determine the distance based on the given force and time.