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Case-based Worksheet for Continuity and Differentiability Class 12

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Case Based Passage

The altitude height

The altitude (height) of a rocket, \(h\) (in meters), \(t\) seconds after launch is given by the piecewise function:

$$ h(t)= \begin{cases}2 t^2 & \text { if } 0 \leq t \leq 20 \\ 100 t-1200 & \text { if } t>20\end{cases} $$
The altitude height
1. Question 1 [1 mark]
Continuity Check: Does the rocket's altitude change continuously at \(t=20\) seconds? Show your work.
2. Question 2 [1 mark]
Velocity: The velocity \(v(t)\) is the derivative of the altitude, \(h^{\prime}(t)\). Find the velocity of the rocket for \(0<t<20\) and for \(t>20\).
3. Question 3 [1 mark]
Differentiability: Is the velocity function continuous at \(t=20\) ? In other words, is the altitude function \(\mathrm{h}(\mathrm{t})\) differentiable at \(t=20\) ? What does this physically mean for the rocket?
4. Question 4 [1 mark]
Acceleration: The acceleration \(a(t)\) is the derivative of velocity, \(v^{\prime}(t)\). What is the rocket's acceleration before and after 20 seconds? What event could this change in acceleration represent?
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About this Case-based Worksheet

This case-based worksheet is designed for Class 12 Maths practice from Continuity and Differentiability Class 12. It uses the question types selected for this worksheet and keeps the preview representative of the complete set.

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