# I have some equations that I would like checked. Thanxs!

1. An automobile starts from rest and accelerates at 3m/s2 for 4 seconds. How fast is it going after acceleration?

3m/s^2 / 4 = .75 m/s

2. If an automobile travels at 30 km/hr. for 2 hours, how far does it go?

d=(30 km/hr)(2 hr)= 60 km

3. At time = 0 an automobile already traveling at 30 km/hr. accelerates at 3m/s2 for 2 seconds. During these two seconds, how far does it go? (This one I don't understand)

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? (This one I don't understand)

## 1. Multiply like in number two

2. Right
3. final velocity^2 = initialvelocity^2 + 2*acceleration*(distance traveled)

-- Solve for distance traveled

4. use above equation and solve for final velocity

## For question 3, to find how far the automobile goes during the two seconds of acceleration, we can use the following equation:

d = v₀t + 0.5at²

Where:
- d is the distance traveled
- v₀ is the initial velocity
- t is the time of acceleration
- a is the acceleration

Since the automobile is already traveling at 30 km/hr (which converts to 8.33 m/s), the initial velocity v₀ would be 8.33 m/s. The time of acceleration (t) is given as 2 seconds, and the acceleration (a) is given as 3 m/s².

Plugging these values into the equation, we get:

d = (8.33 m/s)(2 s) + 0.5(3 m/s²)(2 s)²
d = 16.66 m + 0.5(3 m/s²)(4 s²)
d = 16.66 m + 6 m
d = 22.66 m

Therefore, the automobile travels a distance of 22.66 meters during the two seconds of acceleration.

For question 4, to find the new velocity of the automobile after it has covered 100 meters with an acceleration of 3 m/s², we can use the following equation:

v² = v₀² + 2ad

Where:
- v is the final velocity
- v₀ is the initial velocity
- a is the acceleration
- d is the distance

We are given that the initial velocity (v₀) is 30 km/hr (which converts to 8.33 m/s), the acceleration (a) is 3 m/s², and the distance (d) is 100 meters.

Plugging these values into the equation, we get:

v² = (8.33 m/s)² + 2(3 m/s²)(100 m)
v² = 69.43 m²/s² + 600 m²/s²
v² = 669.43 m²/s²

Taking the square root of both sides, we find:

v = √(669.43 m²/s²)
v ≈ 25.88 m/s

Therefore, the new velocity of the automobile after it has covered 100 meters with an acceleration of 3 m/s² is approximately 25.88 m/s.