The takeoff speed for an Airbus A320 jetliner is 80 m/s. Velocity data measured during takeoff are as shown. Is the jetliner's acceleration constant during takeoff? Explain.

Name: Physics for Scientists and Engineers
Author: Knight Calc
ISBN: 9780137344796

Verified step by step guidance

Step 1: Recall the definition of acceleration. Acceleration is the rate of change of velocity with respect to time, mathematically expressed as \( a = \frac{\Delta v}{\Delta t} \), where \( \Delta v \) is the change in velocity and \( \Delta t \) is the change in time.

Step 2: Use the velocity data provided in the table to calculate the acceleration for each time interval. For example, between \( t = 0 \) and \( t = 10 \), \( \Delta v = v_{x}(10) - v_{x}(0) \) and \( \Delta t = 10 - 0 \). Repeat this calculation for the intervals \( t = 10 \) to \( t = 20 \), and \( t = 20 \) to \( t = 30 \).

Step 3: Compare the calculated acceleration values for each interval. If the acceleration values are the same for all intervals, then the jetliner's acceleration is constant. If the values differ, the acceleration is not constant.

Step 4: Interpret the results. If the acceleration is constant, it indicates uniform motion under constant force. If the acceleration varies, it suggests changes in the forces acting on the jetliner during takeoff.

Step 5: Conclude whether the jetliner's acceleration is constant during takeoff based on the comparison of acceleration values calculated in Step 3.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Acceleration

Acceleration is defined as the rate of change of velocity over time. It can be calculated using the formula a = (v_f - v_i) / t, where v_f is the final velocity, v_i is the initial velocity, and t is the time interval. If the acceleration is constant, the velocity will change linearly over time, resulting in a straight line when plotted on a graph.

Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time, including both speed and direction. In the context of the Airbus A320, the velocity data shows how the speed of the jetliner increases at different time intervals during takeoff. Analyzing these values helps determine if the acceleration is constant or variable.

Graphical Analysis

Graphical analysis involves interpreting data presented in graphical form, such as velocity vs. time graphs. By plotting the given velocity data against time, one can visually assess whether the relationship is linear, indicating constant acceleration, or nonlinear, suggesting varying acceleration. This method is crucial for understanding the dynamics of the jetliner during takeoff.

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