Question

problem 1. maurice is running along parkside avenue with an initial velocity of 2.3 m/s. he travels a displacement of 16 m before reaching a final velocity of 5.7 m/s. calculate maurices acceleration.
problem 2. jade is walking to school with an initial velocity of 3 m/s. she begins to accelerate at a rate of 1.5 m/s² for a time of 5 s. calculate jades final velocity.
problem 3. a limo drives forward with an initial velocity of 3 m/s. it travels a displacement of 90 m in 14 s. determine the final velocity of the limo.
problem 4. a rabbit travels a displacement on 75 m in a time of 10 s before coming to a complete stop. calculate the acceleration of the rabbit.

Explanation:

Problem 1:

Step1: Identify the known - values

Given $v_0 = 2.3\ m/s$, $\Delta x=16\ m$, $v_f = 5.7\ m/s$. Use the formula $v_f^{2}=v_0^{2}+2a\Delta x$.

Step2: Rearrange the formula for acceleration

$a=\frac{v_f^{2}-v_0^{2}}{2\Delta x}$.

Step3: Substitute the values

$a=\frac{(5.7)^{2}-(2.3)^{2}}{2\times16}=\frac{32.49 - 5.29}{32}=\frac{27.2}{32}=0.85\ m/s^{2}$.

Problem 2:

Step1: Identify the known - values

Given $v_0 = 3\ m/s$, $a = 1.5\ m/s^{2}$, $t = 5\ s$. Use the formula $v_f=v_0+at$.

Step2: Substitute the values

$v_f=3+1.5\times5=3 + 7.5=10.5\ m/s$.

Problem 3:

Step1: Identify the known - values

Given $v_0 = 3\ m/s$, $\Delta x = 90\ m$, $t = 14\ s$. First, use the formula $\Delta x=v_0t+\frac{1}{2}at^{2}$ to find $a$.
$90=3\times14+\frac{1}{2}a\times(14)^{2}$
$90 = 42+98a$
$98a=90 - 42$
$98a = 48$
$a=\frac{48}{98}\approx0.49\ m/s^{2}$
Then use $v_f=v_0+at$
$v_f=3+0.49\times14=3 + 6.86 = 9.86\ m/s$.

Problem 4:

Step1: Identify the known - values

Given $\Delta x = 75\ m$, $t = 10\ s$, $v_f = 0\ m/s$. Use the formula $\Delta x=v_0t+\frac{1}{2}at^{2}$ and $v_f=v_0+at$ (where $v_f = 0$ so $v_0=-at$).
Substitute $v_0=-at$ into $\Delta x=v_0t+\frac{1}{2}at^{2}$:
$\Delta x=-at\times t+\frac{1}{2}at^{2}$
$\Delta x=-\frac{1}{2}at^{2}$
$a=-\frac{2\Delta x}{t^{2}}$

Step2: Substitute the values

$a=-\frac{2\times75}{10^{2}}=-\frac{150}{100}=-1.5\ m/s^{2}$.

Answer:

Problem 1: $0.85\ m/s^{2}$
Problem 2: $10.5\ m/s$
Problem 3: $9.86\ m/s$
Problem 4: $-1.5\ m/s^{2}$