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Chapter 2: Problem 3

A car is traveling due west at \(20.0 \mathrm{~m} / \mathrm{s}\). Find the velocity of the car after \(3.00 \mathrm{~s}\) if its acceleration is \(1.0 \mathrm{~m} / \mathrm{s}^{2}\) due west. Assume the acceleration remains constant. a) \(17.0 \mathrm{~m} / \mathrm{s}\) west b) \(17.0 \mathrm{~m} / \mathrm{s}\) east c) \(23.0 \mathrm{~m} / \mathrm{s}\) west d) \(23.0 \mathrm{~m} / \mathrm{s}\) east e) \(11.0 \mathrm{~m} / \mathrm{s}\) south

Short Answer

Expert verified
Answer: The final velocity of the car is \(23.0 \mathrm{~m} / \mathrm{s}\) west.

Step by step solution

01

List the given information

We are given: Initial velocity (v0) = \(20.0 \mathrm{~m} / \mathrm{s}\) (due west) Acceleration (a) = \(1.0 \mathrm{~m} / \mathrm{s}^{2}\) (due west) Time (t) = \(3.00 \mathrm{~s}\)
02

Apply the formula for velocity under constant acceleration

The formula is: \(v = v_0 + at\), where: v = final velocity v0 = initial velocity a = acceleration t = time
03

Plug in the given values and calculate the final velocity

Now, we'll substitute the given values into the formula: \(v = 20.0 \mathrm{~m} / \mathrm{s} \ + (1.0 \mathrm{~m} / \mathrm{s}^{2})(3.00 \mathrm{~s})\) \(v = 20.0 \mathrm{~m} / \mathrm{s} \ + (1.0 \mathrm{~m} / \mathrm{s}^{2})(3.00 \mathrm{~s}) = 20.0 \mathrm{~m} / \mathrm{s} + 3.0 \mathrm{~m} / \mathrm{s} = 23.0 \mathrm{~m} / \mathrm{s}\) The final velocity of the car is \(23.0 \mathrm{~m} / \mathrm{s}\) due west. The correct answer is: c) \(23.0 \mathrm{~m} / \mathrm{s}\) west

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Most popular questions from this chapter

You are driving at \(29.1 \mathrm{~m} / \mathrm{s}\) when the truck ahead of you comes to a halt \(200.0 \mathrm{~m}\) away from your bumper. Your brakes are in poor condition and you decelerate at a constant rate of \(2.4 \mathrm{~m} / \mathrm{s}^{2}\) a) How close do you come to the bumper of the truck? b) How long does it take you to come to a stop?

The position versus time for an object is given as \(x=A t^{4}-B t^{3}+C\) a) What is the instantaneous velocity as a function of time? b) What is the instantaneous acceleration as a function of time?

Which of these statement(s) is (are) true? 1\. An object can have zero acceleration and be at rest. 2\. An object can have nonzero acceleration and be at rest. 3\. An object can have zero acceleration and be in motion. a) 1 only b) 1 and 3 c) 1 and 2 d) \(1,2,\) and 3

The position of an object as a function of time is given as \(x=A t^{3}+B t^{2}+C t+D .\) The constants are \(A=2.1 \mathrm{~m} / \mathrm{s}^{3}\) \(B=1.0 \mathrm{~m} / \mathrm{s}^{2}, C=-4.1 \mathrm{~m} / \mathrm{s},\) and \(D=3 \mathrm{~m}\) a) What is the velocity of the object at \(t=10.0 \mathrm{~s}\) ? b) At what time(s) is the object at rest? c) What is the acceleration of the object at \(t=0.50 \mathrm{~s} ?\) d) Plot the acceleration as a function of time for the time interval from \(t=-10.0 \mathrm{~s}\) to \(t=10.0 \mathrm{~s}\).

A car travels north at \(30.0 \mathrm{~m} / \mathrm{s}\) for \(10.0 \mathrm{~min}\). It then travels south at \(40.0 \mathrm{~m} / \mathrm{s}\) for \(20.0 \mathrm{~min}\). What are the total distance the car travels and its displacement?
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