Answer:
The acceleration of the rocket while the engine is working is 5 meters per square seconds.
Explanation:
Since the rocket accelerates uniformly, the velocity increases linearly and the acceleration ([tex]a[/tex]), measured in meters per second, can be determined by definition of secant line:
[tex]a = \frac{v_{f}-v_{o}}{t_{f}-t_{o}}[/tex] (1)
Where:
[tex]t_{o}[/tex], [tex]t_{f}[/tex] - Initial and final instants, measured in seconds.
[tex]v_{o}[/tex], [tex]v_{f}[/tex] - Initial and final velocities, measured in meters per second.
If we know that [tex]t_{o} = 0\,s[/tex], [tex]t_{f} = 8\,s[/tex], [tex]v_{o} = 0\,\frac{m}{s}[/tex] and [tex]v_{f} = 40\,\frac{m}{s}[/tex], then the acceleration of the rocket while the engine is working:
[tex]a = \frac{40\,\frac{m}{s}-0\,\frac{m}{s} }{8\,s-0\,s}[/tex]
[tex]a = 5\,\frac{m}{s^{2}}[/tex]
The acceleration of the rocket while the engine is working is 5 meters per square seconds.
