A rocket is launched from rest. After 8.0 min, it is 160 Km above the Earth’s surface and is moving at a speed of 7.6 Km/s. Assuming the rocket moves up in a straight line, what are its (a) average velocity and (b) average acceleration?
Average velocity = (vertical distance travelled)/ (480 seconds)
Average acceleration = (velocity change)/(480 seconds)
They have given you all the numbers you need to compute both.
To calculate the average velocity and average acceleration of the rocket, we need to first define the initial and final conditions of its motion.
Given:
Initial position (h1) = 0 Km (since the rocket is launched from rest)
Final position (h2) = 160 Km
Time (t) = 8.0 min = 8.0 × 60 = 480 s
Velocity (v) = 7.6 Km/s
(a) Average Velocity:
Average velocity is the total displacement divided by the total time taken. Displacement is the change in position, which can be calculated as the difference between the final and initial positions.
Displacement (Δh) = h2 - h1 = 160 Km - 0 Km = 160 Km
Average velocity (v_avg) = Δh / t
Substituting the given values:
v_avg = 160 Km / 480 s
v_avg = 1/3 Km/s
Therefore, the average velocity of the rocket is 1/3 Km/s.
(b) Average Acceleration:
Average acceleration is the change in velocity divided by the total time taken. In this case, as the rocket moves up in a straight line, we assume its acceleration to be constant.
Change in velocity (Δv) = v - 0 = 7.6 Km/s
Average acceleration (a_avg) = Δv / t
Substituting the given values:
a_avg = 7.6 Km/s / 480 s
a_avg = 0.01583 Km/s²
Therefore, the average acceleration of the rocket is 0.01583 Km/s².