Question

1. solve for final velocity. 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? 11. an athlete running at 7 m/s accelerates at 2.5 m/s² for 6 seconds. what is the athletes final velocity after the acceleration? 12. an airplane decelerates on the runway at a rate of -4 m/s². if it touches down with a velocity of 60 m/s and slows down, what is its final velocity after 15 seconds?

Explanation:

9.

Step1: Identify the initial - velocity, acceleration and time

The initial velocity \(u = 0\ m/s\) (starts from rest), the acceleration \(a=8\ m/s^{2}\), and the time \(t = 12\ s\).

Step2: Use the equation \(v=u + at\)

Substitute the values into the equation \(v=0+8\times12\).

Step3: Calculate the final velocity

\(v = 96\ m/s\)

Step1: Identify the initial - velocity, acceleration and time

The initial velocity \(u = 2\ m/s\), the acceleration \(a = 3\ m/s^{2}\), and the time \(t = 5\ s\).

Step2: Use the equation \(v=u+at\)

Substitute the values into the equation \(v = 2+3\times5\).

Step3: Calculate the final velocity

First, calculate \(3\times5 = 15\), then \(v=2 + 15=17\ m/s\)

Step1: Identify the initial - velocity, acceleration and time

The initial velocity \(u = 7\ m/s\), the acceleration \(a=2.5\ m/s^{2}\), and the time \(t = 6\ s\).

Step2: Use the equation \(v=u + at\)

Substitute the values into the equation \(v=7+2.5\times6\).

Step3: Calculate the final velocity

First, calculate \(2.5\times6=15\), then \(v = 7+15=22\ m/s\)

Answer:

\(96\ m/s\)

10.