Having trouble determ the formulas for the follow problems.
2. If an automobile travels at 30 km/hr. for 2 hours, how far does it go?
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?
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?
Let D = distance travelled and Vo be the initial velocity, and a be the acceleration
2. D = Vo * t (no acceleration; V remains Vo)
3. D = Vo*t + (1/2) a t^2
Vo = 8 1/3 m/s ; answer will be in meters
4. Vfinal^2 = Vo^2 + 2 a D
Vfinal = Vo + a t,
but you need to solve for t to use the second formula. The two formulas are consistent.
To solve these problems, we need to use some basic formulas from physics. Let's break down each problem and explain the formulas used to find the answer.
Problem 2:
"If an automobile travels at 30 km/hr for 2 hours, how far does it go?"
To find the distance traveled, we can use the formula:
Distance = Speed x Time
In this case, the speed is given as 30 km/hr, and the time is given as 2 hours. We can convert the speed to km/hr to km/min by dividing it by 60:
Speed = 30 km/hr / 60 = 0.5 km/min
Now, we can substitute the values into the formula:
Distance = 0.5 km/min x 120 min = 60 km
Therefore, the automobile goes 60 km.
Problem 3:
"At time = 0, an automobile already traveling at 30 km/hr accelerates at 3m/s^2 for 2 seconds. During these two seconds, how far does it go?"
To find the distance traveled during acceleration, we can use the formula:
Distance = Initial Velocity x Time + (1/2) x Acceleration x Time^2
In this case, the initial velocity is given as 30 km/hr, which can be converted to m/s by multiplying it by 1000/3600:
Initial Velocity = 30 km/hr x (1000 m/km) / (3600 s/hr) = 8.33 m/s
Acceleration is given as 3 m/s^2, and time is given as 2 seconds.
Substituting the values into the formula:
Distance = 8.33 m/s x 2 s + (1/2) x 3 m/s^2 x (2 s)^2
= 16.66 m + (1/2) x 3 m/s^2 x 4 s^2
= 16.66 m + 6 m
= 22.66 m
Therefore, the automobile goes 22.66 meters during the acceleration.
Problem 4:
"An automobile is traveling at 30 km/hr. It accelerates at 3 m/s^2 until it has covered 100 meters. What is its new velocity?"
To find the new velocity, we can use the formula:
Final Velocity^2 = Initial Velocity^2 + 2 x Acceleration x Distance
In this case, the initial velocity is given as 30 km/hr, which can be converted to m/s by multiplying it by 1000/3600:
Initial Velocity = 30 km/hr x (1000 m/km) / (3600 s/hr) = 8.33 m/s
Acceleration is given as 3 m/s^2, and the distance covered is given as 100 meters.
Substituting the values into the formula and solving for Final Velocity:
Final Velocity^2 = 8.33 m/s^2 + 2 x 3 m/s^2 x 100 m
Final Velocity^2 = 8.33 m/s^2 + 600 m^2/s^2
Final Velocity^2 = 608.33 m^2/s^2
Taking the square root of both sides to find the Final Velocity:
Final Velocity = √(608.33 m^2/s^2)
Final Velocity ≈ 24.68 m/s
Therefore, the new velocity of the automobile is approximately 24.68 m/s.