Question

1. a bullet train accelerates uniformly at 2 m/s², increasing its speed from 30 m/s to 60 m/s. how long does it take for the train? 7. a motorcycle accelerates at 4 m/s², increasing its velocity from 15 m/s to 35 m/s. how long does it take for the motorcycle? 8. an object is dropped from a great height and accelerates do to gravity at 9.8 m/s². how long does it take to reach a velocity of 49 m/s?

Explanation:

Step1: Identify the kinematic - equation

We use the kinematic equation $v = v_0+at$. In all three cases, the initial velocity $v_0$, final velocity $v$, and acceleration $a$ are given, and we need to solve for time $t$. The formula can be re - arranged to $t=\frac{v - v_0}{a}$.

Step2: Solve for question 6

Given $v_0 = 30\ m/s$, $v = 60\ m/s$, and $a = 2\ m/s^2$. Substitute into the formula $t=\frac{v - v_0}{a}=\frac{60 - 30}{2}$.
$t=\frac{30}{2}=15\ s$.

Step3: Solve for question 7

Given $v_0 = 15\ m/s$, $v = 35\ m/s$, and $a = 4\ m/s^2$. Substitute into the formula $t=\frac{v - v_0}{a}=\frac{35 - 15}{4}$.
$t=\frac{20}{4}=5\ s$.

Step4: Solve for question 8

Given $v_0 = 0\ m/s$ (dropped object), $v = 49\ m/s$, and $a = 9.8\ m/s^2$. Substitute into the formula $t=\frac{v - v_0}{a}=\frac{49-0}{9.8}$.
$t = 5\ s$.

Answer:

1. $15\ s$
2. $5\ s$
3. $5\ s$