On Fig. 1.4, sketch the speed-time graph of the rocket for the first 12 minutes. You do not need to give values for the speed.

The resultant force is the net upward force. The forces acting are the upward thrust from the engine and the downward weight of the rocket.
Resultant Force = Thrust - Weight

Thrust = Resultant Force + Weight

Given: Resultant Force = $50\,000 \, \text{N}$ (upwards), Weight = $400\,000 \, \text{N}$ (downwards).

The thrust produced by the rocket engine is $\boxed{450\,000 \, \text{N}}$.

Newton's Second Law states that $F = ma$, where $F$ is the resultant force, $m$ is the mass, and $a$ is the acceleration.

Given: Resultant Force ($F$) = $50\,000 \, \text{N}$, Mass ($m$) = $40\,000 \, \text{kg}$.

The acceleration of the rocket is $\boxed{1.25 \, \text{m/s}^2}$.

The x-axis represents time (in minutes) and the y-axis represents speed.

1.3 for each time interval.

• 0 to 4 minutes: uniform acceleration. This is represented by a straight line with a positive slope, starting from zero speed.
• 4 to 6 minutes: increasing acceleration. This means the slope of the graph is increasing. The line will curve upwards, becoming steeper.
• 6 to 10 minutes: decreasing acceleration. This means the slope of the graph is decreasing. The line will curve downwards, becoming less steep.
• 10 to 12 minutes: constant speed. This means the acceleration is zero. The line will be horizontal.

Here is the sketch of the speed-time graph:

      ^ Speed
      |
      |      /
      |     / \
      |    /   \
      |   /     \
      |  /       -----
      | /
      |/
      +---------------------> Time (minutes)
      0  4   6   10  12

(Note: This is a textual representation. In a proper sketch, the curves for increasing and decreasing acceleration would be smooth, and the lines would connect seamlessly.)