13. a plane accelerates down a runway at 3 m/s² for 10 seconds before takeoff. what is the final velocity of…
13. a plane accelerates down a runway at 3 m/s² for 10 seconds before takeoff. what is the final velocity of the plane? 14. a motorcycle moving at 25 m/s slows down to 10 m/s in 3 seconds. what is the acceleration? 15. a car is initially at 10 m/s. it accelerates at 2 m/s² for 6 seconds. what is its final velocity? 16. an object is dropped from a height and reaches 24 m/s after 3 seconds. what is the objects average acceleration? 17. a soccer ball is kicked and accelerates at 5 m/s² for 0.6 seconds. if it started at 2 m/s, what is its final speed? 18. a rocket is launched upward. it starts from rest and accelerates at 9 m/s² for 12 seconds. what is its final velocity? 19. a skateboarder slows from 8 m/s to a stop in 4 seconds. what is the acceleration? 20. a cyclist is riding at 10 m/s when a pedestrian steps into the bike lane 15 meters ahead. the cyclist brakes with an acceleration of -2.5 m/s². will the cyclist stop in time, or hit the pedestrian? (assume instant reaction time and constant deceleration. show calculations and explain.) 21. a train is moving at 25 m/s when the conductor sees a barrier 200 meters ahead. the train begins braking immediately with a constant acceleration of -1.2 m/s². will the train stop before hitting the barrier? (show your work and explain your reasoning.) 22. a motorcycle is cruising at 18 m/s when the rider sees a red light 40 meters away. the rider brakes with a constant acceleration of -6 m/s². does the motorcycle stop before the intersection, or does it run the red light?(include all work and a short explanation.)
Answer
Explanation:
Step1: Identify the formula
Use the formula $v = v_0+at$, where $v$ is final - velocity, $v_0$ is initial - velocity, $a$ is acceleration, and $t$ is time.
Step2: Substitute the values
Given $v_0 = 10$ m/s, $a = 2$ m/s², and $t = 6$ s. Then $v=10 + 2\times6$.
Step3: Calculate the result
$v=10 + 12=22$ m/s.
Answer:
22 m/s
Explanation:
Step1: Identify the formula
The formula for average acceleration is $a=\frac{v - v_0}{t}$, where $v$ is final - velocity, $v_0$ is initial - velocity (since it is dropped, $v_0 = 0$ m/s), $a$ is acceleration, and $t$ is time.
Step2: Substitute the values
Given $v = 24$ m/s, $v_0 = 0$ m/s, and $t = 3$ s. Then $a=\frac{24 - 0}{3}$.
Step3: Calculate the result
$a = 8$ m/s².
Answer:
8 m/s²
Explanation:
Step1: Identify the formula
Use the formula $v = v_0+at$, where $v$ is final - speed, $v_0$ is initial - speed, $a$ is acceleration, and $t$ is time.
Step2: Substitute the values
Given $v_0 = 2$ m/s, $a = 5$ m/s², and $t = 0.6$ s. Then $v=2+5\times0.6$.
Step3: Calculate the result
$v=2 + 3=5$ m/s.
Answer:
5 m/s
Explanation:
Step1: Identify the formula
Use the formula $v = v_0+at$, where $v$ is final - velocity, $v_0$ is initial - velocity (starts from rest, so $v_0 = 0$ m/s), $a$ is acceleration, and $t$ is time.
Step2: Substitute the values
Given $a = 9$ m/s², $t = 12$ s, and $v_0 = 0$ m/s. Then $v=0+9\times12$.
Step3: Calculate the result
$v = 108$ m/s.
Answer:
108 m/s
Explanation:
Step1: Identify the formula
The formula for acceleration is $a=\frac{v - v_0}{t}$, where $v$ is final - velocity ($v = 0$ m/s as it stops), $v_0$ is initial - velocity, $a$ is acceleration, and $t$ is time.
Step2: Substitute the values
Given $v_0 = 8$ m/s, $v = 0$ m/s, and $t = 4$ s. Then $a=\frac{0 - 8}{4}$.
Step3: Calculate the result
$a=-2$ m/s².
Answer:
-2 m/s²
Explanation:
Step1: Identify the formula
Use the formula $v^{2}=v_0^{2}+2ax$ to find the stopping - distance $x$, where $v$ is final - velocity ($v = 0$ m/s), $v_0$ is initial - velocity, $a$ is acceleration.
Step2: Rearrange the formula for $x$
$x=\frac{v^{2}-v_0^{2}}{2a}$.
Step3: Substitute the values
Given $v_0 = 10$ m/s, $v = 0$ m/s, and $a=-2.5$ m/s². Then $x=\frac{0 - 10^{2}}{2\times(-2.5)}=\frac{- 100}{-5}=20$ m. Since $20>15$, the cyclist will hit the pedestrian.
Answer:
The cyclist will hit the pedestrian.
Explanation:
Step1: Identify the formula
Use the formula $v^{2}=v_0^{2}+2ax$ to find the stopping - distance $x$, where $v$ is final - velocity ($v = 0$ m/s), $v_0$ is initial - velocity, $a$ is acceleration.
Step2: Rearrange the formula for $x$
$x=\frac{v^{2}-v_0^{2}}{2a}$.
Step3: Substitute the values
Given $v_0 = 25$ m/s, $v = 0$ m/s, and $a=-1.2$ m/s². Then $x=\frac{0 - 25^{2}}{2\times(-1.2)}=\frac{-625}{-2.4}\approx260.42$ m. Since $260.42>200$, the train will hit the barrier.
Answer:
The train will hit the barrier.
Explanation:
Step1: Identify the formula
Use the formula $v^{2}=v_0^{2}+2ax$ to find the stopping - distance $x$, where $v$ is final - velocity ($v = 0$ m/s), $v_0$ is initial - velocity, $a$ is acceleration.
Step2: Rearrange the formula for $x$
$x=\frac{v^{2}-v_0^{2}}{2a}$.
Step3: Substitute the values
Given $v_0 = 18$ m/s, $v = 0$ m/s, and $a=-6$ m/s². Then $x=\frac{0 - 18^{2}}{2\times(-6)}=\frac{-324}{-12}=27$ m. Since $27<40$, the motorcycle will stop before the intersection.
Answer:
The motorcycle will stop before the intersection.