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Chapter 2: Problem 55

A car starts from rest and accelerates at \(10.0 \mathrm{~m} / \mathrm{s}^{2}\) How far does it travel in 2.00 s?

Short Answer

Expert verified
Answer: The car travels a distance of 20.0 meters in 2.00 seconds.

Step by step solution

01

List given information

The problem provides us with the following information: - The car starts from rest, meaning its initial velocity is 0: \(v_0 = 0 \mathrm{~m}/\mathrm{s}\) - The car accelerates at a constant rate: \(a = 10.0 \mathrm{~m}/\mathrm{s}^{2}\) - We need to find the distance traveled in a given time: \(t = 2.00 \mathrm{~s}\)
02

Use the kinematic equation to determine the distance traveled

Since we have the initial velocity, acceleration, and time, we can use the following kinematic equation to find the distance traveled: $$ d = v_0t + \frac{1}{2}at^2 $$ This equation states that the distance traveled (d) is equal to the product of the initial velocity (v_0) and time (t) plus one-half the product of the acceleration (a) and the square of the time (t^2).
03

Substitute the given values and solve for the distance

Substitute the given values into the equation: $$ d = (0 \mathrm{~m}/\mathrm{s})(2.00 \mathrm{~s}) + \frac{1}{2}(10.0 \mathrm{~m}/\mathrm{s}^{2})(2.00 \mathrm{~s})^2 $$ Now, simplify the equation and solve for the distance: $$ d = 0 + (10.0 \mathrm{~m}/\mathrm{s}^{2})(4.00 \mathrm{~s}^2)/2 $$ $$ d = (20.0 \mathrm{~m}/\mathrm{s}^{2})(2.00 \mathrm{~s}^2) $$ $$ d = 20.0 \mathrm{~m} $$
04

State the final answer

The car travels a distance of \(20.0\) meters in \(2.00\) seconds.

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Most popular questions from this chapter

A car travels at 22.0 mph for 15.0 min and 35.0 mph for \(30.0 \mathrm{~min}\). How far does it travel overall? a) \(23.0 \mathrm{~m}\) b) \(3.70 \cdot 10^{4} \mathrm{~m}\) c) \(1.38 \cdot 10^{3} \mathrm{~m}\) d) \(3.30 \cdot 10^{2} \mathrm{~m}\)

You are flying on a commercial airline on your way from Houston, Texas, to Oklahoma City, Oklahoma. Your pilot announces that the plane is directly over Austin, Texas, traveling at a constant speed of \(245 \mathrm{mph}\), and will be flying directly over Dallas, Texas, \(362 \mathrm{~km}\) away. How long will it be before you are directly over Dallas, Texas?

A fighter jet lands on the deck of an aircraft carrier. It touches down with a speed of \(70.4 \mathrm{~m} / \mathrm{s}\) and comes to a complete stop over a distance of \(197.4 \mathrm{~m}\). If this process happens with constant deceleration, what is the speed of the jet \(44.2 \mathrm{~m}\) before its final stopping location?

Two cars are traveling at the same speed, and the drivers hit the brakes at the same time. The deceleration of one car is double that of the other. By what factor does the time required for that car to come to a stop compare with that for the other car?

An object is thrown upward with a speed of \(28.0 \mathrm{~m} / \mathrm{s}\). How long does it take it to reach its maximum height?
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