19. Acceleration, a, in meters per second squared (m/s²), 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/s², of an object with a beginning velocity of 14 m/s and end velocity of 8 m/s over a time of 4 seconds?
Answer: B
The acceleration of the object is -1.5 m/s².
To find the acceleration, we apply the formula a = (V2 - V1)/t. Substituting the values V1 = 14 m/s, V2 = 8 m/s, and t = 4 seconds yields a = (8 - 14) / 4, which simplifies to -1.5 m/s².
A) 1.5
Option A is incorrect because it represents a positive value of acceleration, which would imply the object is speeding up. However, in this scenario, the object is actually slowing down, as the final velocity (8 m/s) is less than the initial velocity (14 m/s).
B) -1.5
Option B is correct as it accurately reflects the calculation of acceleration. The change in velocity is negative (8 - 14 = -6), and dividing by the time of 4 seconds results in an acceleration of -1.5 m/s², indicating that the object is decelerating.
C) 4.5
Option C is incorrect because it suggests a significant positive acceleration, which does not align with the scenario described. The object is not increasing its speed; rather, it is losing speed, making this option inconsistent with the calculation.
D) -12
Option D is incorrect as it indicates a much larger negative acceleration than what is calculated. The change in velocity divided by time does not support such a steep decline, as the actual calculation yields -1.5 m/s².
Conclusion
The correct answer is definitively -1.5 m/s², as it accurately represents the object's deceleration based on the initial and final velocities and the time interval given. All other options fail to reflect the actual change in motion, either by suggesting an incorrect direction of acceleration or by miscalculating the magnitude.