Question

a rocket blasts off. in 10.0 seconds it is at 10,000 ft, travelling at 3600 mph. assuming the direction is up, calculate the acceleration. (hint: the rocket is not under constant acceleration).
○ 200. ft/s²
○ 528 ft/s²
○ 5280 ft/s²
○ 100 ft/s²

Explanation:

Step1: Convert velocity to ft/s

We know that 1 mile = 5280 feet and 1 hour = 3600 seconds. So, to convert 3600 mph to ft/s, we use the conversion factors:
\[
v = 3600 \, \frac{\text{miles}}{\text{hour}} \times \frac{5280 \, \text{ft}}{1 \, \text{mile}} \times \frac{1 \, \text{hour}}{3600 \, \text{s}}
\]
Simplifying this, the 3600 in the numerator and denominator cancels out, leaving \(v = 5280 \, \text{ft/s}\).

Step2: Calculate acceleration

Acceleration \(a\) is the change in velocity over time. Assuming the initial velocity \(u = 0\) (starts from rest), time \(t = 10.0 \, \text{s}\), and final velocity \(v = 5280 \, \text{ft/s}\). The formula for acceleration is \(a=\frac{v - u}{t}\).
Substituting the values:
\[
a=\frac{5280 - 0}{10.0}=\frac{5280}{10.0} = 528 \, \text{ft/s}^2
\]

Answer:

528 ft/s² (corresponding to the option "528 ft/s²")