Question

part b: acceleration, change in velocity, time
use the formula a = δv/t. show your work.

1. a car speeds up from 0 m/s to 20 m/s in 5 seconds. what is its acceleration?
2. a ball slows from 15 m/s to 0 m/s in 3 seconds. what is its acceleration?
3. a train accelerates at 2 m/s² for 10 seconds. what is its change in velocity?
4. a roller coaster increases velocity from 10 m/s to 30 m/s in 4 seconds. find acceleration.
5. a motorcycle goes from 12 m/s to 24 m/s with an acceleration of 3 m/s². how long does this take?
6. a plane accelerates from 0 to 60 m/s in 15 seconds. what is its acceleration?
7. a bus slows from 25 m/s to 10 m/s in 5 seconds. what is its acceleration?
8. a rocket accelerates at 5 m/s² for 12 seconds. what is its change in velocity?
9. a runner increases velocity from 4 m/s to 10 m/s in 3 seconds. what is their acceleration?
10. a car experiences an acceleration of 2.5 m/s² for 8 seconds. what is its change in velocity?

Explanation:

Step1: Identify the formula

The formula for acceleration is $a=\frac{\Delta v}{t}$, where $a$ is acceleration, $\Delta v$ is change in velocity, and $t$ is time. For finding change in velocity $\Delta v = a\times t$, and for finding time $t=\frac{\Delta v}{a}$.

Step2: Solve problem 11

Given initial velocity $u = 0$ m/s, final velocity $v=20$ m/s, and $t = 5$ s. $\Delta v=v - u=20 - 0=20$ m/s. Then $a=\frac{\Delta v}{t}=\frac{20}{5}=4$ m/s².

Step3: Solve problem 12

Given $u = 15$ m/s, $v = 0$ m/s, $t = 3$ s. $\Delta v=v - u=0 - 15=- 15$ m/s. Then $a=\frac{\Delta v}{t}=\frac{-15}{3}=-5$ m/s².

Step4: Solve problem 13

Given $a = 2$ m/s² and $t = 10$ s. Using $\Delta v=a\times t$, we get $\Delta v=2\times10 = 20$ m/s.

Step5: Solve problem 14

Given $u = 10$ m/s, $v = 30$ m/s, $t = 4$ s. $\Delta v=v - u=30 - 10 = 20$ m/s. Then $a=\frac{\Delta v}{t}=\frac{20}{4}=5$ m/s².

Step6: Solve problem 15

Given $u = 12$ m/s, $v = 24$ m/s, $a = 3$ m/s². $\Delta v=v - u=24 - 12 = 12$ m/s. Then $t=\frac{\Delta v}{a}=\frac{12}{3}=4$ s.

Step7: Solve problem 16

Given $u = 0$ m/s, $v = 60$ m/s, $t = 15$ s. $\Delta v=v - u=60 - 0=60$ m/s. Then $a=\frac{\Delta v}{t}=\frac{60}{15}=4$ m/s².

Step8: Solve problem 17

Given $u = 25$ m/s, $v = 10$ m/s, $t = 5$ s. $\Delta v=v - u=10 - 25=-15$ m/s. Then $a=\frac{\Delta v}{t}=\frac{-15}{5}=-3$ m/s².

Step9: Solve problem 18

Given $a = 5$ m/s² and $t = 12$ s. Using $\Delta v=a\times t$, we get $\Delta v=5\times12 = 60$ m/s.

Step10: Solve problem 19

Given $u = 4$ m/s, $v = 10$ m/s, $t = 3$ s. $\Delta v=v - u=10 - 4 = 6$ m/s. Then $a=\frac{\Delta v}{t}=\frac{6}{3}=2$ m/s².

Step11: Solve problem 20

Given $a = 2.5$ m/s² and $t = 8$ s. Using $\Delta v=a\times t$, we get $\Delta v=2.5\times8 = 20$ m/s.

Answer:

1. $4$ m/s²
2. $-5$ m/s²
3. $20$ m/s
4. $5$ m/s²
5. $4$ s
6. $4$ m/s²
7. $-3$ m/s²
8. $60$ m/s
9. $2$ m/s²
10. $20$ m/s