Question

1. a car traveling at a speed of 30 m/s encounters an emergency and comes to a complete stop. how much time will it take for the car to stop if it decelerates at -4 m/s²?
2. if a car can go from 0 to 60 mi/hr in 8 seconds, what would be its final speed after 5 seconds if its starting speed were 50 mi/hr?
3. a cart rolling down an incline for 5 seconds has an acceleration of 4 m/s². if the cart has a beginning speed of 2 m/s, what is its final speed?

Explanation:

Problem 4

Step1: Identify the formula

Use the formula \(v = v_0+at\), where \(v = 0\) (final velocity, car stops), \(v_0=30\ m/s\) (initial velocity), \(a=- 4\ m/s^{2}\) (acceleration), and \(t\) is the time we want to find.

Step2: Rearrange the formula for \(t\)

From \(v = v_0+at\), we get \(t=\frac{v - v_0}{a}\).

Step3: Substitute the values

Substitute \(v = 0\), \(v_0 = 30\ m/s\), and \(a=-4\ m/s^{2}\) into the formula: \(t=\frac{0 - 30}{-4}=\frac{-30}{-4}=7.5\ s\)

Step1: Convert units (if needed)

First, find the acceleration. The change in velocity \(\Delta v=60 - 0=60\ mi/hr\), and \(\Delta t = 8\ s\). The acceleration \(a=\frac{\Delta v}{\Delta t}=\frac{60}{8}=7.5\ mi/hr/s\)

Step2: Use the formula \(v = v_0+at\)

Here, \(v_0 = 50\ mi/hr\), \(a = 7.5\ mi/hr/s\), and \(t = 5\ s\). Substitute into \(v=v_0+at\): \(v=50+7.5\times5\)

Step3: Calculate the value

\(v=50 + 37.5=87.5\ mi/hr\)

Step1: Use the formula \(v = v_0+at\)

Given \(v_0 = 2\ m/s\), \(a = 4\ m/s^{2}\), and \(t = 5\ s\)

Step2: Substitute the values

\(v=2+4\times5\)

Step3: Calculate the value

\(v=2 + 20=22\ m/s\)

Answer:

\(7.5\ s\)

Problem 5