Question

using the information about time and velocity in the table, determine the acceleration of the airplane as it travels down the runway.
time\tvelocity
0 s\t+10 m/s
1 s\t+18 m/s
2 s\t+26 m/s
3 s\t+34 m/s
4 s\t+42 m/s
a 10.5 m/s²
b 32 m/s²
c 13 m/s²
d 8 m/s²

Explanation:

Step1: Recall acceleration formula

Acceleration \( a = \frac{\Delta v}{\Delta t} \), where \( \Delta v \) is change in velocity and \( \Delta t \) is change in time.

Step2: Calculate \( \Delta v \) and \( \Delta t \)

Take initial time \( t_1 = 0 \, \text{s} \), initial velocity \( v_1 = 10 \, \text{m/s} \); final time \( t_2 = 4 \, \text{s} \), final velocity \( v_2 = 42 \, \text{m/s} \).
\( \Delta v = v_2 - v_1 = 42 - 10 = 32 \, \text{m/s} \)
\( \Delta t = t_2 - t_1 = 4 - 0 = 4 \, \text{s} \)

Step3: Compute acceleration

\( a = \frac{\Delta v}{\Delta t} = \frac{32}{4} = 8 \, \text{m/s}^2 \) (Or check with adjacent times: e.g., \( t=0 \) to \( t=1 \): \( \Delta v = 18 - 10 = 8 \, \text{m/s} \), \( \Delta t = 1 \, \text{s} \), \( a = 8 \, \text{m/s}^2 \); same for other intervals.)

Answer:

D. \( 8 \, \text{m/s}^2 \)