Constant acceleration: An airplane that is flying level needs to accelerate from a speed of 2.00 × 10² m/s to a speed of 2.40 × 10² m/s while it flies a distance of 1.20 km. What must be the acceleration of the plane? A) 4.44 m/s² B) 2.45 m/s² C) 7.33 m/s² D) 5.78 m/s² E) 1.34 m/s²

Question

Quizplus · Accepted Answer

Using the equation: 
$v_f^2 = v_i^2 + 2ad$
where:
$v_f$ = final velocity = 2.40 × 10S1U1P12S1S1P0 m/s
$v_i$ = initial velocity = 2.00 × 10S1U1P12S1S1P0 m/s
$d$ = distance = 1.20 km = 1.20 × 10S3U1P0S1S
$a$ = acceleration (what we're solving for)

Converting distance to meters:
$d = 1.20 × 10S3U1P0S1S = 1.20 × 10S3U1P03S1S = 1200 m$

Substituting into the equation and solving for $a$:
$(2.40 × 10S1U1P12S1S1P0)^2 = (2.00 × 10S1U1P12S1S1P0)^2 + 2a(1200)$
$5.76 × 10S2U1P24S1S1P0 = 4.00 × 10S2U1P24S1S1P0 + 2400a$
$1.76 × 10S2U1P24S1S1P0 = 2400a$
$a = \frac{1.76 × 10S2U1P24S1S1P0}{2400} = 7.33 m/sS1U1P12S1S1P0$

Therefore, the acceleration of the plane must be 7.33 m/sS1U1P12S1S1P0.

Constant Acceleration: an Airplane That Is Flying Level Needs to Accelerate