Which equation is most likely used to determine the acceleration from a $v$
$a=\frac{t}{\Delta v}$
$m=\frac{y_2-y_1}{x_2-x_1}$
$a=\frac{\Delta v}{m}$
$m=\frac{x_2-x_1}{y_2-y_1}$
Answer (1)
The equation that most likely determines acceleration is a = m Δ v , where a is acceleration, Δ v is the change in velocity, and m represents a quantity related to time. a = m Δ v
Explanation
Understanding Acceleration We are asked to identify the equation that is most likely used to determine acceleration. Acceleration is defined as the rate of change of velocity with respect to time. This means we are looking for an equation that expresses acceleration ( a ) as the change in velocity ( Δ v ) divided by a quantity that represents time or is related to time.
Analyzing the Equations Let's examine the given options:
a = Δ v t : This equation represents time divided by the change in velocity, which is the inverse of acceleration.
m = x 2 − x 1 y 2 − y 1 : This equation calculates the slope of a line and is not directly related to acceleration.
a = m Δ v : This equation represents the change in velocity divided by a variable m . If m represents time or a quantity related to time, this equation could represent acceleration.
m = y 2 − y 1 x 2 − x 1 : This equation also calculates the slope of a line (reciprocal of the previous slope equation) and is not directly related to acceleration.
Identifying the Correct Equation Comparing the options with the definition of acceleration, the equation a = m Δ v is the most likely candidate, where m could represent time or a quantity related to time.
Conclusion Therefore, the most likely equation used to determine acceleration is a = m Δ v .
Examples
Understanding acceleration is crucial in many real-world scenarios. For instance, when designing a car, engineers need to calculate how quickly the car can accelerate from 0 to 60 mph. This involves using the formula a = Δ t Δ v , where Δ v is the change in velocity and Δ t is the time it takes to achieve that change. Similarly, pilots use acceleration calculations to determine the takeoff distance required for an aircraft. These calculations ensure safety and efficiency in transportation systems.
