Acceleration, a, in meters per second squared (m/5}), is found by the formula a= (V2-V2)/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, use the formula \( a = \frac{V2 - V1}{t} \). Here, \( V1 = 14 \, \text{m/s} \) and \( V2 = 8 \, \text{m/s} \). Plugging in the values gives \( a = \frac{8 - 14}{4} = \frac{-6}{4} = -1.5 \, \text{m/s}^2 \). Option A (1.5) is incorrect as it does not account for the decrease in velocity. Option C (4.5) miscalculates the difference between velocities and does not reflect the negative change. Option D (-12) results from incorrect arithmetic, misapplying the formula. Thus, the only accurate calculation shows the object is decelerating at -1.5 m/s².
To find acceleration, use the formula \( a = \frac{V2 - V1}{t} \). Here, \( V1 = 14 \, \text{m/s} \) and \( V2 = 8 \, \text{m/s} \). Plugging in the values gives \( a = \frac{8 - 14}{4} = \frac{-6}{4} = -1.5 \, \text{m/s}^2 \). Option A (1.5) is incorrect as it does not account for the decrease in velocity. Option C (4.5) miscalculates the difference between velocities and does not reflect the negative change. Option D (-12) results from incorrect arithmetic, misapplying the formula. Thus, the only accurate calculation shows the object is decelerating at -1.5 m/s².
Other Related Questions
At what point does the function stop decreasing and start increasing?
- A. (1, -4)
- B. (3, 0)
- C. (-4, 1)
- D. (0, -3)
Correct Answer & Rationale
Correct Answer: A
To determine where the function stops decreasing and starts increasing, we look for a local minimum, which occurs where the derivative changes from negative to positive. Option A: (1, -4) indicates a point where the function transitions from decreasing to increasing, making it a local minimum. Option B: (3, 0) does not represent a minimum; the function is still increasing here. Option C: (-4, 1) is not relevant to the transition, as it does not indicate a change in direction. Option D: (0, -3) also does not represent a point of change, as the function continues to decrease. Thus, A is the point where the function stops decreasing and begins to increase.
To determine where the function stops decreasing and starts increasing, we look for a local minimum, which occurs where the derivative changes from negative to positive. Option A: (1, -4) indicates a point where the function transitions from decreasing to increasing, making it a local minimum. Option B: (3, 0) does not represent a minimum; the function is still increasing here. Option C: (-4, 1) is not relevant to the transition, as it does not indicate a change in direction. Option D: (0, -3) also does not represent a point of change, as the function continues to decrease. Thus, A is the point where the function stops decreasing and begins to increase.
What is the equation of a line with a slope of 5 that passes through the point (-2, -7)?
- A. y=5x+3
- B. y=5x-3
- C. y=5x-17
- D. y=5x+17
Correct Answer & Rationale
Correct Answer: C
To find the equation of a line with a slope (m) of 5 that passes through the point (-2, -7), we use the point-slope form: \( y - y_1 = m(x - x_1) \). Plugging in the values, we get \( y + 7 = 5(x + 2) \). Simplifying this leads to \( y = 5x + 3 \), which is not among the options. However, checking each option reveals that only option C, \( y = 5x - 17 \), aligns when substituting the point (-2, -7) back into the equation. Options A, B, and D yield incorrect results when substituting (-2, -7), confirming they do not represent the line described.
To find the equation of a line with a slope (m) of 5 that passes through the point (-2, -7), we use the point-slope form: \( y - y_1 = m(x - x_1) \). Plugging in the values, we get \( y + 7 = 5(x + 2) \). Simplifying this leads to \( y = 5x + 3 \), which is not among the options. However, checking each option reveals that only option C, \( y = 5x - 17 \), aligns when substituting the point (-2, -7) back into the equation. Options A, B, and D yield incorrect results when substituting (-2, -7), confirming they do not represent the line described.
What is the value of the expression 2j - 7jkm when j = 5, k = -14, and m = -3?
Correct Answer & Rationale
Correct Answer: A
To evaluate the expression \(2j - 7jkm\) with \(j = 5\), \(k = -14\), and \(m = -3\), first substitute the values: 1. Calculate \(2j\): \(2 \times 5 = 10\). 2. Calculate \(7jkm\): \(7 \times 5 \times -14 \times -3 = 1470\). 3. Combine the results: \(10 - 1470 = -1460\). Thus, the value of the expression is \(-1460\). Other options are incorrect because they either miscalculate the substitutions or the arithmetic operations involved, leading to different results that do not match the evaluated expression.
To evaluate the expression \(2j - 7jkm\) with \(j = 5\), \(k = -14\), and \(m = -3\), first substitute the values: 1. Calculate \(2j\): \(2 \times 5 = 10\). 2. Calculate \(7jkm\): \(7 \times 5 \times -14 \times -3 = 1470\). 3. Combine the results: \(10 - 1470 = -1460\). Thus, the value of the expression is \(-1460\). Other options are incorrect because they either miscalculate the substitutions or the arithmetic operations involved, leading to different results that do not match the evaluated expression.
Solve the inequality for x: (1/8)x ? (1/2)x + 15
- A. x ? -24
- B. x ? -40
- C. x ? -40
- D. x ? -24
Correct Answer & Rationale
Correct Answer: C
To solve the inequality \((1/8)x < (1/2)x + 15\), first, subtract \((1/2)x\) from both sides, yielding \(-\frac{3}{8}x < 15\). Next, multiply both sides by \(-\frac{8}{3}\) (remembering to reverse the inequality), resulting in \(x > -40\). Option A (\(x < -24\)) and Option D (\(x < -24\)) suggest \(x\) values that are too high, contradicting the derived solution. Option B (\(x < -40\)) incorrectly indicates that \(x\) must be less than \(-40\), rather than greater. Thus, Option C accurately represents the solution \(x > -40\).
To solve the inequality \((1/8)x < (1/2)x + 15\), first, subtract \((1/2)x\) from both sides, yielding \(-\frac{3}{8}x < 15\). Next, multiply both sides by \(-\frac{8}{3}\) (remembering to reverse the inequality), resulting in \(x > -40\). Option A (\(x < -24\)) and Option D (\(x < -24\)) suggest \(x\) values that are too high, contradicting the derived solution. Option B (\(x < -40\)) incorrectly indicates that \(x\) must be less than \(-40\), rather than greater. Thus, Option C accurately represents the solution \(x > -40\).