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Chapter 4: Problem 27

What is the acceleration of an automobile of mass $1.40 \times 10^{3} \mathrm{kg}\( when it is subjected to a forward force of \)3.36 \times 10^{3} \mathrm{N} ?$

Short Answer

Expert verified
Answer: The acceleration of the automobile is approximately \(2.4 \, \mathrm{m/s^2}\).

Step by step solution

01

Write down the given values

The mass of the automobile is given as \(1.40 \times 10^{3}\mathrm{kg}\), and the forward force acting upon it is \(3.36 \times 10^{3}\mathrm{N}\).
02

Use Newton's Second Law of Motion

Newton's second law states that the force acting on an object is equal to its mass times its acceleration: $$F = m \cdot a$$
03

Rearrange the equation for acceleration

To find the acceleration, we need to rearrange the equation to solve for a: $$a = \frac{F}{m}$$
04

Plug in the given values and solve for acceleration

Now we can plug in the given values into the equation: $$a = \frac{3.36 \times 10^{3}\mathrm{N}}{1.40 \times 10^{3}\mathrm{kg}}$$ […]
05

Calculate the acceleration

When we plug in the values and calculate the result: $$a \approx 2.4 \, \mathrm{m/s^2}$$ The acceleration of the automobile is approximately \(2.4 \, \mathrm{m/s^2}\).

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Most popular questions from this chapter

A crate full of artichokes rests on a ramp that is inclined \(10.0^{\circ}\) above the horizontal. Give the direction of the normal force and the friction force acting on the crate in each of these situations. (a) The crate is at rest. (b) The crate is being pushed and is sliding up the ramp. (c) The crate is being pushed and is sliding down the ramp.
An airplane of mass \(2800 \mathrm{kg}\) has just lifted off the runway. It is gaining altitude at a constant \(2.3 \mathrm{m} / \mathrm{s}\) while the horizontal component of its velocity is increasing at a rate of $0.86 \mathrm{m} / \mathrm{s}^{2} .\( Assume \)g=9.81 \mathrm{m} / \mathrm{s}^{2} .$ (a) Find the direction of the force exerted on the airplane by the air. (b) Find the horizontal and vertical components of the plane's acceleration if the force due to the air has the same magnitude but has a direction \(2.0^{\circ}\) closer to the vertical than its direction in part (a).
An engine pulls a train of 20 freight cars, each having a mass of $5.0 \times 10^{4} \mathrm{kg}$ with a constant force. The cars move from rest to a speed of \(4.0 \mathrm{m} / \mathrm{s}\) in \(20.0 \mathrm{s}\) on a straight track. Ignoring friction, what is the force with which the 10th car pulls the 11th one (at the middle of the train)? (school bus)
A rope is attached from a truck to a \(1400-\mathrm{kg}\) car. The rope will break if the tension is greater than \(2500 \mathrm{N}\) Ignoring friction, what is the maximum possible acceleration of the truck if the rope does not break? Should the driver of the truck be concerned that the rope might break?
A man lifts a 2.0 -kg stone vertically with his hand at a constant upward acceleration of \(1.5 \mathrm{m} / \mathrm{s}^{2} .\) What is the magnitude of the total force of the man's hand on the stone?
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