The position from its starting point of a small plane preparing for takeoff is given by meters ( is measured in seconds). What is the
acceleration of the plane?

Ask by Colon Salazar. in the United States

Mar 31,2025

Question

The position from its starting point of a small plane preparing for takeoff is given by $$ x(t)=1.63 t^{2} $$ meters ( $$ t $$ is measured in seconds). What is the acceleration of the plane?

UpStudy AI · Accepted Answer

To find the acceleration of the plane, we need to find the second derivative of the position function $$ x(t) $$ with respect to time $$ t $$.

Given:
$$ x(t) = 1.63t^2 $$

The acceleration of the plane is the second derivative of the position function with respect to time, which is denoted as $$ a(t) $$.

To find the acceleration, we will differentiate the position function twice with respect to time.
Evaluate the derivative by following steps:
- step0: Evaluate the derivative:
  $$\frac{d}{dt}\left(\frac{d}{dt}\left(1.63t^{2}\right)\right)$$
- step1: Calculate:
  $$\frac{d}{dt}\left(3.26t\right)$$
- step2: Use differentiation rules:
  $$3.26\times \frac{d}{dt}\left(t\right)$$
- step3: Find the derivative:
  $$3.26\times 1$$
- step4: Calculate:
  $$3.26$$
The acceleration of the plane is $$ a(t) = 3.26 $$ meters per second squared.
The acceleration of the plane is 3.26 meters per second squared.

The position from its starting point of a small plane preparing for takeoff is given by meters ( is measured in seconds). What is the
acceleration of the plane?

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The position from its starting point of a small plane preparing for takeoff is given by meters ( is measured in seconds). What is the acceleration of the plane?