Question

1. Starting from rest, a particle moving in a straight line has an acceleration of $a = (2t^2 - 10) \text{ m/s}^2$, where t is in seconds. What is the particle's velocity when $t = 6 \text{ s}$, and what is its position when $t = 10 \text{ s}$? 2. The acceleration of a rocket traveling upward is given by $a = 18 + 0.06s \text{ m/s}^2$ where s is in meters. Determine the time needed for the rocket to reach an altitude of $s = 200 \text{ m}$. Initially, $v = 0$ and $s = 0$ when $t = 0$. 3. The velocity of a car is plotted as shown. Determine the total distance the car moves until it stops ($t = 100 \text{ s}$). Construct the a-t graph.

          1. Starting from rest, a particle moving in a straight line has an acceleration of $a = (2t^2 - 10) \text{ m/s}^2$, where t is in seconds. What is the particle's velocity when $t = 6 \text{ s}$, and what is its position when $t = 10 \text{ s}$?
2. The acceleration of a rocket traveling upward is given by $a = 18 + 0.06s \text{ m/s}^2$ where s is in meters. Determine the time needed for the rocket to reach an altitude of $s = 200 \text{ m}$. Initially, $v = 0$ and $s = 0$ when $t = 0$.
3. The velocity of a car is plotted as shown. Determine the total distance the car moves until it stops ($t = 100 \text{ s}$). Construct the a-t graph.

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Added by Michele V.

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