6 A van moves from rest on a straight horizontal road.
- In a simple model, the first 30 seconds of the motion are represented by three separate stages, each lasting 10 seconds and each with a constant acceleration.
During the first stage, the van accelerates from rest to a velocity of \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
During the second stage, the van accelerates from \(4 \mathrm {~ms} ^ { - 1 }\) to \(12 \mathrm {~ms} ^ { - 1 }\).
During the third stage, the van accelerates from \(12 \mathrm {~ms} ^ { - 1 }\) to \(16 \mathrm {~ms} ^ { - 1 }\).
- Sketch a velocity-time graph to represent the motion of the van during the first 30 seconds of its motion.
- Find the total distance that the van travels during the 30 seconds.
- Find the average speed of the van during the 30 seconds.
- Find the greatest acceleration of the van during the 30 seconds.
- In another model of the 30 seconds of the motion, the acceleration of the van is assumed to vary during the first and third stages of the motion, but to be constant during the second stage, as shown in the velocity-time graph below.
\includegraphics[max width=\textwidth, alt={}, center]{c220e6c4-2676-4022-8301-7d720dc082b2-5_554_1138_1432_539}
The velocity of the van takes the same values at the beginning and the end of each stage of the motion as in part (a).
- State, with a reason, whether the distance travelled by the van during the first 10 seconds of the motion in this model is greater or less than the distance travelled during the same time interval in the model in part (a).
- Give one reason why this model represents the motion of the van more realistically than the model in part (a).