Question

1. a rocket accelerates from rest with an acceleration of 8 m/s² for 12 seconds. what is its final velocity after accelerating? 10. a skateboarder starts at a velocity of 2 m/s and accelerates down a ramp at 3 m/s² for 5 seconds. what is the final velocity of the skateboarder?

Explanation:

Step1: Recall the kinematic - equation

The kinematic equation for final velocity is $v = v_0+at$, where $v$ is the final velocity, $v_0$ is the initial velocity, $a$ is the acceleration, and $t$ is the time.

Step2: Solve problem 9

Given $v_0 = 0$ m/s (starts from rest), $a = 8$ m/s², and $t = 12$ s.
Substitute the values into the equation: $v=0 + 8\times12$.
$v = 96$ m/s.

Step3: Solve problem 10

Given $v_0 = 2$ m/s, $a = 3$ m/s², and $t = 5$ s.
Substitute the values into the equation: $v=2+3\times5$.
$v=2 + 15$.
$v = 17$ m/s.

Answer:

1. 96 m/s
2. 17 m/s