At launch a rocket ship weighs 4.5 million pounds. When it is launched from rest, it takes 8.00 s to reach 161 km/h; at the end of the first 1.00 min, its speed is 1610 km/h. (a) What is the average acceleration (in m/s2) of the rocket (i) during the first 8.00 s and (ii) between 8.00 s and the end of the first 1.00 min?

Verified step by step guidance

1. Convert the initial speed from km/h to m/s: 161 km/h = 161 \times \frac{1000}{3600} m/s.
2. Convert the final speed from km/h to m/s: 1610 km/h = 1610 \times \frac{1000}{3600} m/s.
3. Calculate the average acceleration during the first 8.00 s using the formula: a = \frac{\Delta v}{\Delta t}, where \Delta v is the change in velocity (final velocity - initial velocity, here initial velocity is 0) and \Delta t is the time interval.
4. Calculate the average acceleration between 8.00 s and the end of the first 1.00 min (60 s) using the same formula: a = \frac{\Delta v}{\Delta t}, where \Delta v is the change in velocity (final velocity at 60 s - velocity at 8 s) and \Delta t is the time interval (60 s - 8 s).
5. Ensure all units are consistent when performing calculations, particularly time in seconds and velocity in m/s.

Key Concepts

Acceleration

Acceleration is defined as the rate of change of velocity over time. It is a vector quantity, meaning it has both magnitude and direction. In this context, it can be calculated using the formula a = (v_f - v_i) / t, where v_f is the final velocity, v_i is the initial velocity, and t is the time taken for that change. Understanding acceleration is crucial for analyzing the rocket's motion during its launch.

Units of Measurement

In physics, it is essential to use consistent units when performing calculations. The problem involves weights in pounds and speeds in kilometers per hour, which need to be converted to standard SI units (meters, kilograms, seconds) for accurate calculations. For instance, 1 pound is approximately 0.453592 kilograms, and 1 kilometer per hour is approximately 0.277778 meters per second. Proper unit conversion ensures that the results are meaningful and comparable.

Average vs. Instantaneous Values

Average values represent the total change over a period divided by the time taken, while instantaneous values refer to the measurement at a specific moment. In this question, average acceleration is calculated for two distinct time intervals: the first 8 seconds and from 8 seconds to 1 minute. Recognizing the difference between these two types of measurements is vital for accurately interpreting the rocket's performance during its launch phases.