4. An automobile is traveling at 30 km/hr. It accelerates at 3 m/s2 until it has covered 100 meters.. What is its new velocity?
I asked my teacher on what formula I should use and said I should use this one: V^2= Vo^2+2ax (V^2 is the velocit, Vo is the initial velocity, a is accerlation and x distance
I used that formuala and got 668.90 m/s
V^2= (8.3 m/s)^2+2(3m/s^2)(100 m)=668.90 m/s
I converted 30km/hr by doing this:
(30 km/hr)(1000 m/km)(1hr/3600)=8.3m/s
That answer my teacher said I was suppose to get is 25.9 m/s and that I could convert it to 93.2 km/hr.
Your 668.90 is for V^2. Take the square root of that to get 25.9. You just omitted a step.
To solve this problem, you correctly converted the initial velocity of the automobile from 30 km/hr to 8.3 m/s. Then, you applied the formula V^2 = Vo^2 + 2ax, where V represents the final velocity, Vo is the initial velocity, a is the acceleration, and x is the distance. You substituted the given values into the equation, with Vo = 8.3 m/s, a = 3 m/s^2, and x = 100 m.
However, there seems to be a mistake in your calculation. Let's go through the correct calculation using the given formula:
V^2 = (8.3 m/s)^2 + 2(3 m/s^2)(100 m)
V^2 = 68.89 m^2/s^2 + 600 m^2/s^2
V^2 = 668.89 m^2/s^2
To find the new velocity, V, we take the square root of V^2:
V = √(668.89 m^2/s^2)
V ≈ 25.9 m/s
Therefore, the new velocity of the automobile after accelerating is approximately 25.9 m/s.
To convert this velocity to kilometers per hour, you can use the conversion factor:
(25.9 m/s) × (3600 s/hr) ÷ (1000 m/km) ≈ 93.2 km/hr
So, the new velocity can also be expressed as approximately 93.2 km/hr.
In conclusion, the correct answer for the new velocity of the automobile is approximately 25.9 m/s or 93.2 km/hr.