Find the airplane's acceleration and time?

Question

An airplane flies eastward and always accelerates at a constant rate. At one position along its path it has a velocity of 33.5 m/s, it then flies a further distance of 43300 m and afterwards its velocity is 46.7 m/s. Find the airplane\'s acceleration and calculate how much time elapses while the airplane covers those 43300 m.

Answer 1

x_i = 0 m

x_f = 43,300 m

v_i = 33.5 m/s

v_f = 46.7 m/s

s (displacement) = x_f - x_i = 43,300 m

 

v_f² = v_i² + 2as

⇒ a = (v_f² - v_i²) / 2s

= ((46.7 m/s)² - (33.5 m/s)²) / 2(43,300 m)

= (1058.64 m²/s²) / 2(43,300 m)

= 0.012224 m/s²

 

a = (v_f - v_i) / t

⇒ t = (v_f - v_i) / a

= ((46.7 m/s) - (33.5 m/s)) / (0.012224 m/s²)

= 1079.8 s

Answer 2

Meg, there's a formula in physics that relates to an object's constant acceleration in relation to its change in velocity and position. When there is a change in velocity due to an acceleration, there has to be a force due to Newton's Second Law of Motion, that is, the sum of the forces equals mass times acceleration. There's another term called work in which is the product of force and distance in which an object goes. I apologize for confusing work and potential energy. Potential and Kinetic energy is related to gravity in which PE = mgh and KE = 1/2*mv^2.

 

Logan is correct when he made the correction in using the formula:

 

v2^2=v1^2+2as

 

v1 = initial velocity

v2=final velocity

a=acceleration

s=displacement distance 

 

Again, I apologize for this confusion.