Question

Example Given: An aircraft is accelerating whilst taxiing. It starts with a speed of 2 m/s. The acceleration is given as a =30v−4[ m/s2] Find: Determine the velocity and the distance covered after 40 s Plan: For the determining of the velocity acknowledge the fact that the acceleration has beer given as a function of velocity ⇒ use a=dv/dt For determining the distance acknowledge that we are now looking for distance s while a has been given ⇒ use a ds =vd d

Answer 1

The student's physics problem involves determining the velocity and distance covered by an accelerating aircraft using differential equations due to a variable acceleration that depends on velocity.

Step-by-step explanation:

The student is tasked with determining the velocity and the distance covered by an aircraft that is accelerating while taxiing over a period of 40 seconds. Given that the initial speed is 2 m/s and the acceleration is a function of velocity expressed as a = 30v - 4 m/s2, we can use the differential equation a = dv/dt to solve for velocity. For distance, we integrate velocity with respect to time, using the a ds = v dv relationship.

To solve for velocity, integrate the acceleration with respect to time. Since the acceleration is given in terms of velocity, the integration will include separating variables and using limits of integration corresponding to the given time. Next, solve for the distance covered using the velocity expression you've found, integrating it over the time interval given.

Unfortunately, the example solution strategy for calculating the final velocity and acceleration does not apply here because the acceleration is not constant; it's a function of velocity. We cannot use the formulas v = vo + at or s = vo * t + 0.5 * a * t2 directly in this context since those are valid for constant acceleration scenarios.