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
Laura walks every evening on the edges of a sports field near her house. The field is in the shape of a rectangle 300 feet (ft) long and 200 ft wide, so 1 lap on the edges of the field is 1,000 ft. She enters through a gate at point G, located exactly halfway along the length of the field.
Type your answer in the box. You may use numbers, a decimal point (.), and/or negative sign (-) in your answer.
One evening on her walk, Laura walks across the field from point W back to the gate at point G. What is the distance she walks, in feet, from point W to point G?
Correct Answer & Rationale
Correct Answer: 250
To determine the distance Laura walks from point W to gate G, we can use the Pythagorean theorem. The field is a rectangle, and point W is at one corner. The length from W to G is half the length of the field (150 ft) and the width of the field (200 ft). Calculating the distance: Distance = √(150² + 200²) = √(22500 + 40000) = √62500 = 250 ft. Other options are incorrect because they do not accurately reflect the geometric relationship of the points. Distances such as 300 ft or 200 ft misinterpret the diagonal distance, while any number below 250 fails to account for both dimensions of the rectangle.
To determine the distance Laura walks from point W to gate G, we can use the Pythagorean theorem. The field is a rectangle, and point W is at one corner. The length from W to G is half the length of the field (150 ft) and the width of the field (200 ft). Calculating the distance: Distance = √(150² + 200²) = √(22500 + 40000) = √62500 = 250 ft. Other options are incorrect because they do not accurately reflect the geometric relationship of the points. Distances such as 300 ft or 200 ft misinterpret the diagonal distance, while any number below 250 fails to account for both dimensions of the rectangle.
A shipping box for a refrigerator is shaped like a rectangular prism. The box has a depth of 34.25 inches (in.), a height of 69.37 in., and a width of 32.62 in. To the nearest hundredth cubic inch, what is the volume of the shipping bax?
- A. 2,262.85
- B. 77,502.59
- C. 136.24
- D. 25,834.20
Correct Answer & Rationale
Correct Answer: B
To determine the volume of a rectangular prism, the formula \( V = \text{length} \times \text{width} \times \text{height} \) is applied. Given the dimensions—depth (length) of 34.25 in., width of 32.62 in., and height of 69.37 in.—the calculation yields a volume of approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, indicating a miscalculation. Option C (136.24) is implausibly low, likely resulting from using incorrect units or dimensions. Option D (25,834.20) is also incorrect, as it does not reflect the correct multiplication of the given dimensions. Thus, only option B accurately represents the calculated volume.
To determine the volume of a rectangular prism, the formula \( V = \text{length} \times \text{width} \times \text{height} \) is applied. Given the dimensions—depth (length) of 34.25 in., width of 32.62 in., and height of 69.37 in.—the calculation yields a volume of approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, indicating a miscalculation. Option C (136.24) is implausibly low, likely resulting from using incorrect units or dimensions. Option D (25,834.20) is also incorrect, as it does not reflect the correct multiplication of the given dimensions. Thus, only option B accurately represents the calculated volume.
The mass of an amoeba is approximately 4.0 × 10^(-6) grams. Approximately how many amoebas are present in a sample that weighs 1 gram?
- A. 2.5 × 10^5
- B. 4.0 × 10^7
- C. 4.0 × 10^5
- D. 2.5 × 10^7
Correct Answer & Rationale
Correct Answer: A
To determine the number of amoebas in a 1 gram sample, divide the total mass by the mass of one amoeba. The mass of an amoeba is 4.0 × 10^(-6) grams. Thus, the calculation is: 1 gram / (4.0 × 10^(-6) grams/amoeba) = 2.5 × 10^5 amoebas. Option B (4.0 × 10^7) is incorrect as it suggests a significantly larger quantity, likely resulting from a miscalculation. Option C (4.0 × 10^5) overestimates the number of amoebas by a factor of 2, while option D (2.5 × 10^7) also miscalculates, indicating confusion in the division process.
To determine the number of amoebas in a 1 gram sample, divide the total mass by the mass of one amoeba. The mass of an amoeba is 4.0 × 10^(-6) grams. Thus, the calculation is: 1 gram / (4.0 × 10^(-6) grams/amoeba) = 2.5 × 10^5 amoebas. Option B (4.0 × 10^7) is incorrect as it suggests a significantly larger quantity, likely resulting from a miscalculation. Option C (4.0 × 10^5) overestimates the number of amoebas by a factor of 2, while option D (2.5 × 10^7) also miscalculates, indicating confusion in the division process.
What is the volume, in cubic inches, of the pyramid?
- A. 21,600
- B. 1,440
- C. 7,200
- D. 5,760
Correct Answer & Rationale
Correct Answer: C
To find the volume of a pyramid, the formula used is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). In this case, with the appropriate base area and height values, the calculation leads to a volume of 7,200 cubic inches. Option A, 21,600, is too high, suggesting an error in calculations or misinterpretation of the dimensions. Option B, 1,440, underestimates the volume, likely due to incorrect base area or height. Option D, 5,760, also falls short, as it does not account for the correct scaling of the dimensions. Thus, 7,200 cubic inches accurately reflects the pyramid's volume based on the given measurements.
To find the volume of a pyramid, the formula used is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). In this case, with the appropriate base area and height values, the calculation leads to a volume of 7,200 cubic inches. Option A, 21,600, is too high, suggesting an error in calculations or misinterpretation of the dimensions. Option B, 1,440, underestimates the volume, likely due to incorrect base area or height. Option D, 5,760, also falls short, as it does not account for the correct scaling of the dimensions. Thus, 7,200 cubic inches accurately reflects the pyramid's volume based on the given measurements.