Question

exit ticket 9.17
physics
september 17, 2025
2 kinematic equations
\\(\delta x = \frac{(v_f + v_0)t}{2}\\)
\\(v_f = v_0+at\\)
problem 1. a ram is running with an initial velocity of 2 m/s. it accelerates at a rate of 0.5 m/s² for a time of 7 s. calculate the final velocity of the ram.
problem 2. a whale with an initial velocity of 4 m/s. it travels a displacement of 100 m. if the final velocity of the whale is 15 m/s, calculate the amount of time it was swimming.

Explanation:

Step1: Identify the kinematic - equation

We use the equation $v_f=v_0 + at$ for Problem 1. Given $v_0 = 2\ m/s$, $a=0.5\ m/s^2$, and $t = 7\ s$.

Step2: Substitute the values

$v_f=2+0.5\times7$
$v_f=2 + 3.5$
$v_f=5.5\ m/s$

For Problem 2, we use the equation $\Delta x=\frac{(v_f + v_0)t}{2}$. We need to solve for $t$.

Step3: Rearrange the equation for $t$

From $\Delta x=\frac{(v_f + v_0)t}{2}$, we get $t=\frac{2\Delta x}{v_f + v_0}$. Given $\Delta x = 100\ m$, $v_0=4\ m/s$, and $v_f = 15\ m/s$.

Step4: Substitute the values for Problem 2

$t=\frac{2\times100}{15 + 4}$
$t=\frac{200}{19}\approx10.53\ s$

Answer:

Problem 1: The final velocity of the ram is $5.5\ m/s$.
Problem 2: The time the whale was swimming is $\frac{200}{19}\ s\approx10.53\ s$.