Question

a passenger jet needs to reach a speed of 100 m/s on the runway for takeoff. if the runway is 2.5×10³ m long, what minimum average acceleration from rest is needed? a. 0.040 m/s² b. 2.0 m/s² c. 4.0 m/s² d. 10 m/s²

Explanation:

Step1: Identify the kinematic - equation

We use the equation $v^{2}=v_{0}^{2}+2ax$, where $v$ is the final velocity, $v_{0}$ is the initial velocity, $a$ is the acceleration, and $x$ is the displacement. Given $v_{0} = 0$ (starts from rest), $v = 100\ m/s$, and $x=2.5\times10^{3}\ m$.

Step2: Rearrange the equation for acceleration

From $v^{2}=v_{0}^{2}+2ax$, with $v_{0} = 0$, the equation becomes $a=\frac{v^{2}}{2x}$.

Step3: Substitute the values

Substitute $v = 100\ m/s$ and $x = 2.5\times10^{3}\ m$ into the formula: $a=\frac{100^{2}}{2\times2.5\times10^{3}}=\frac{10000}{5000}=2.0\ m/s^{2}$.

Answer:

B. $2.0\ m/s^{2}$