/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 A \(970-\mathrm{kg}\) car starts... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 13

A \(970-\mathrm{kg}\) car starts from rest on a horizontal roadway and accelerates eastward for \(5.00 \mathrm{~s}\) when it reaches a speed of \(25.0 \mathrm{~m} / \mathrm{s}\). What is the average force exerted on the car during this time?

Short Answer

Expert verified
The average force exerted on the car during this time can be found by multiplying the car's acceleration by its mass. Apply the values found and calculated to get the final answer.

Step by step solution

01

Compute the acceleration of the car

The car's speed changes from 0 \(\mathrm{m/s}\) to 25.0 \(\mathrm{m/s}\) in 5.00 s. Apply the formula \(a=\Delta v/\Delta t\) to find the acceleration. Here \(\Delta v\) is the change in velocity, which is final velocity minus initial velocity, and \(\Delta t\) is the time interval, 5.00 s. So the acceleration \(a\) is (25.0 \(\mathrm{m/s}\) - 0 \(\mathrm{m/s}\)) / 5.00 s.
02

Calculate the average force

Knowing the acceleration and the mass of the car, we can use the second law of Newton, \(F = ma\), to compute the force. Substitute \(m = 970 \, \mathrm{kg}\) and the acceleration \(a\) found in Step 1 into this equation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Acceleration
In physics, acceleration is a measure of how quickly an object changes its velocity. It's a vector quantity, which means it has both magnitude and direction. The concept of acceleration is fundamental when it comes to understanding motion because it describes the rate at which an object speeds up or slows down.

To calculate acceleration, you use the formula:
Once you understand the how and why of acceleration, you can apply this knowledge in various domains of physics, such as mechanics, aerodynamics, and even space travel! Remember, an object can be accelerating even if it's not speeding up; slowing down or changing direction also involves acceleration.
Newton's Second Law
A key principle in physics is Newton's second law of motion. This law states that the acceleration of an object depends on two variables: the net force acting upon the object and the mass of the object. The law is usually formulated as:
Once you understand that the net force on an object is equal to the product of the object's mass and its acceleration, you can predict how an object will move under certain forces. This relationship is a key concept when solving physics problems and is especially important in engineering, where ensuring structural integrity and functionality often relies on understanding how forces interact with materials.
Change in Velocity
In our problem, the change in velocity, denoted as For example, when a car speeds up from 0 to 25.0 m/s, that entire change is its change in velocity. This information gives us a base for calculating acceleration and, eventually, the force. Recognizing the importance of these foundational concepts will allow students to tackle more complex dynamics problems with confidence.

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Most popular questions from this chapter

A van accelerates down a hill (Fig. P4.73), going from rest to \(30.0 \mathrm{~m} / \mathrm{s}\) in \(6.00 \mathrm{~s}\). During the acceleration, atoy \((m=0.100 \mathrm{~kg})\) hangs by a string from the van's ceiling. The acceleration is such that the string remains perpendicular to the ceiling. Determine (a) the angle \(\theta\) and (b) the tension in the string.

A boat moves through the water with two forces acting on it. One is a \(2000-\mathrm{N}\) forward push by the water on the propeller, and the other is a \(1800-\mathrm{N}\) resistive force due to the water around the bow. (a) What is the acceleration of the \(1000-\mathrm{kg}\) boat? (b) If it starts from rest, how far will the boat move in \(10.0 \mathrm{~s}\) ? (c) What will its velocity be at the end of that time?

Consider a solid metal sphere (S) a few centimeters in diameter and a feather (F). For each quantity in the list that follows, indicate whether the quantity is the same, greater, or lesser in the case of \(\mathrm{S}\) or in that of \(\mathrm{F}\). Explain in each case why you gave the answer you did. Here is the list: (a) the gravitational force, (b) the time it will take to fall a given distance in air, (c) the time it will take to fall a given distance in vacuum, (d) the total force on the object when falling in vacuum.

An inquisitive physics student, wishing to combine pleasure with scientific inquiry, rides on a roller coaster sitting on a bathroom scale. (Do not try this yourself on a roller coaster that forbids loose, heavy packages.) The bottom of the seat in the roller-coaster car is in a plane parallel to the track. The seat has a perpendicular back and a seat belt that fits around the student's chest in a plane parallel to the bottom of the seat. The student lifts his feet from the floor so that the scale reads his weight, \(200 \mathrm{lb}\), when the car is horizontal. At one point during the ride, the car zooms with negligible friction down a straight slope inclined at \(30.0^{\circ}\) below the horizontal. What does the scale read at that point?

A \(3.00-\mathrm{kg}\) block starts from rest at the top of a \(30.0^{\circ}\) incline and slides \(2.00 \mathrm{~m}\) down the incline in \(1.50 \mathrm{~s}\). Find (a) the acceleration of the block, (b) the coefficient of kinetic friction between the block and the incline, (c) the frictional force acting on the block, and (d) the speed of the block after it has slid \(2.00 \mathrm{~m}\).
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