Acceleration, a, in meters per second squared (m/s^2), is found by the formula a = (V2 - V1)/t where V1, is the beginning velocity, V2 is the end velocity, and t is time. What is the acceleration, in m/s^2, of an object with a beginning velocity of 14 m/s and end velocity of 8 m/s over a time of 4 seconds?
- A. 1.5
- B. -1.5
- C. 4.5
- D. -12
Correct Answer & Rationale
Correct Answer: B
To find acceleration using the formula \( a = \frac{(V2 - V1)}{t} \), substitute the values: \( V1 = 14 \, \text{m/s} \), \( V2 = 8 \, \text{m/s} \), and \( t = 4 \, \text{s} \). This results in \( a = \frac{(8 - 14)}{4} = \frac{-6}{4} = -1.5 \, \text{m/s}^2 \). Option A (1.5) is incorrect as it does not account for the decrease in velocity. Option C (4.5) miscalculates the difference and time. Option D (-12) incorrectly computes the acceleration by misapplying the formula or misinterpreting the values. Thus, the only accurate calculation reflects a deceleration, resulting in -1.5 m/s².
To find acceleration using the formula \( a = \frac{(V2 - V1)}{t} \), substitute the values: \( V1 = 14 \, \text{m/s} \), \( V2 = 8 \, \text{m/s} \), and \( t = 4 \, \text{s} \). This results in \( a = \frac{(8 - 14)}{4} = \frac{-6}{4} = -1.5 \, \text{m/s}^2 \). Option A (1.5) is incorrect as it does not account for the decrease in velocity. Option C (4.5) miscalculates the difference and time. Option D (-12) incorrectly computes the acceleration by misapplying the formula or misinterpreting the values. Thus, the only accurate calculation reflects a deceleration, resulting in -1.5 m/s².
Other Related Questions
How many more miles did the space shuttle Discovery travel than the space shuttle Atlantis?
- A. 274,100,000 miles
- B. 274,100 miles
- C. 22.3 miles
- D. 22,300,000 miles
Correct Answer & Rationale
Correct Answer: D
To determine the difference in miles traveled between the space shuttles Discovery and Atlantis, one must subtract the total miles of Atlantis from Discovery. The calculation reveals that Discovery traveled 22,300,000 miles more than Atlantis, making option D the accurate choice. Option A, 274,100,000 miles, is excessively high and does not reflect the actual difference. Option B, 274,100 miles, is too low and misrepresents the scale of space travel. Option C, 22.3 miles, is trivial and fails to capture the vast distances involved in space missions. Thus, option D accurately represents the significant difference in miles traveled.
To determine the difference in miles traveled between the space shuttles Discovery and Atlantis, one must subtract the total miles of Atlantis from Discovery. The calculation reveals that Discovery traveled 22,300,000 miles more than Atlantis, making option D the accurate choice. Option A, 274,100,000 miles, is excessively high and does not reflect the actual difference. Option B, 274,100 miles, is too low and misrepresents the scale of space travel. Option C, 22.3 miles, is trivial and fails to capture the vast distances involved in space missions. Thus, option D accurately represents the significant difference in miles traveled.
Simplify: (3x - 5) + (-7x + 2)
- A. -4x^2 - 3
- B. -4x - 3
- C. 28
- D. -4x^2 - 10
Correct Answer & Rationale
Correct Answer: B
To simplify the expression (3x - 5) + (-7x + 2), first combine like terms. Start with the x terms: 3x + (-7x) results in -4x. Next, combine the constant terms: -5 + 2 equals -3. Thus, the simplified expression is -4x - 3, matching option B. Option A, -4x^2 - 3, incorrectly includes an x^2 term that does not exist in the original expression. Option C, 28, is unrelated to the simplification process. Option D, -4x^2 - 10, also includes an incorrect x^2 term and miscalculates the constants.
To simplify the expression (3x - 5) + (-7x + 2), first combine like terms. Start with the x terms: 3x + (-7x) results in -4x. Next, combine the constant terms: -5 + 2 equals -3. Thus, the simplified expression is -4x - 3, matching option B. Option A, -4x^2 - 3, incorrectly includes an x^2 term that does not exist in the original expression. Option C, 28, is unrelated to the simplification process. Option D, -4x^2 - 10, also includes an incorrect x^2 term and miscalculates the constants.
What is the value of 0.6 - (0.7)(1.4)?
- A. -0.38
- B. -0.14
- C. -0.42
- D. -1.5
Correct Answer & Rationale
Correct Answer: A
To solve 0.6 - (0.7)(1.4), first calculate the product (0.7)(1.4), which equals 0.98. Subtracting this from 0.6 gives 0.6 - 0.98 = -0.38. Option B (-0.14) results from an incorrect subtraction, possibly miscalculating the product. Option C (-0.42) suggests an error in understanding the subtraction process, likely misapplying the negative sign. Option D (-1.5) is far too low and indicates a misunderstanding of basic arithmetic operations. Thus, the correct calculation leads to -0.38, confirming option A as the accurate answer.
To solve 0.6 - (0.7)(1.4), first calculate the product (0.7)(1.4), which equals 0.98. Subtracting this from 0.6 gives 0.6 - 0.98 = -0.38. Option B (-0.14) results from an incorrect subtraction, possibly miscalculating the product. Option C (-0.42) suggests an error in understanding the subtraction process, likely misapplying the negative sign. Option D (-1.5) is far too low and indicates a misunderstanding of basic arithmetic operations. Thus, the correct calculation leads to -0.38, confirming option A as the accurate answer.
Solve the equation for x: (2x-3)/5 = x/10
- A. 2
- B. 3
- C. 1\5
- D. 10
Correct Answer & Rationale
Correct Answer: A
To solve the equation \((2x-3)/5 = x/10\), first eliminate the fractions by multiplying both sides by 10, resulting in \(2(2x - 3) = x\). Simplifying gives \(4x - 6 = x\). Rearranging leads to \(4x - x = 6\), or \(3x = 6\), giving \(x = 2\). Option B (3) does not satisfy the equation when substituted back. Option C (1/5) results in a negative left side, while Option D (10) leads to an incorrect balance in the original equation. Thus, the only solution that holds true is \(x = 2\).
To solve the equation \((2x-3)/5 = x/10\), first eliminate the fractions by multiplying both sides by 10, resulting in \(2(2x - 3) = x\). Simplifying gives \(4x - 6 = x\). Rearranging leads to \(4x - x = 6\), or \(3x = 6\), giving \(x = 2\). Option B (3) does not satisfy the equation when substituted back. Option C (1/5) results in a negative left side, while Option D (10) leads to an incorrect balance in the original equation. Thus, the only solution that holds true is \(x = 2\).