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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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