Question

problem 6. a barrel is rolled down a hill with an initial velocity of 2.0 m/s. the barrel accelerates at a rate of 1.2 m/s². how much time passes before the barrel reaches a final velocity of 9.7 m/s?
problem 7. an arrow is launched with an initial velocity of 3.2 m/s. it travels a displacement of 60 m in 10 s. calculate the final velocity of the arrow.
problem 8. a sponge is knocked off a table with an initial velocity of 1.3 m/s. it accelerates at a rate of 10 m/s² until it reaches a final velocity of 55 m/s. calculate the amount of time that the sponge was falling.
problem 9. a giant squid is moving through the pacific ocean with an initial velocity of 11 m/s. it accelerates at a rate of 3 m/s² for 19 s. calculate the final velocity of the squid.
problem 10. the initial velocity of a racecar is 6 m/s. the car speeds up for 20 s until it reaches a final velocity of 16 m/s. calculate the displacement of the racecar.

Explanation:

Problem 6

Step1: Identify the formula

We use the formula $v = v_0+at$, where $v$ is final - velocity, $v_0$ is initial - velocity, $a$ is acceleration and $t$ is time. We can re - arrange it for $t$: $t=\frac{v - v_0}{a}$.

Step2: Substitute the values

Given $v_0 = 2.0\ m/s$, $v = 9.7\ m/s$ and $a=1.2\ m/s^2$. Then $t=\frac{9.7 - 2.0}{1.2}=\frac{7.7}{1.2}\approx6.42\ s$.

Step1: Identify the formula

We use the formula $\Delta x=\frac{(v + v_0)t}{2}$, where $\Delta x$ is displacement, $v$ is final - velocity, $v_0$ is initial - velocity and $t$ is time. We can re - arrange it for $v$: $v=\frac{2\Delta x}{t}-v_0$.

Step2: Substitute the values

Given $v_0 = 3.2\ m/s$, $\Delta x = 60\ m$ and $t = 10\ s$. Then $v=\frac{2\times60}{10}-3.2=12 - 3.2 = 8.8\ m/s$.

Step1: Identify the formula

We use the formula $v = v_0+at$, and re - arrange it for $t$: $t=\frac{v - v_0}{a}$.

Step2: Substitute the values

Given $v_0 = 1.3\ m/s$, $v = 55\ m/s$ and $a = 10\ m/s^2$. Then $t=\frac{55 - 1.3}{10}=\frac{53.7}{10}=5.37\ s$.

Answer:

$6.42\ s$

Problem 7