Could you please check my answers and units. Thanxs!
1. An automobile starts from rest and accelerates at 3m/s2 for 4 seconds. How fast is it going after acceleration?
-I got 12 m/s
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?
-I got 12 m/s
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?
- 6030 (not sure about units)
3. Change 30km/hr to m/s
30km/hr*1hr/3600sec*1000m/km
then
distance=vi*t + 1/2 at^2
4. You need to work the units. Chang 30km/hr to meters/second. Then work it, keeping the units in the problem until you find out what your answer is, numerically, and the units.
I am still not understanding. Like for number 3, this is as far as I got 30km/36000000. Then for number 4, would it be similar as to number 3? Also, did I get number 1 correct?
1. To calculate the final speed of the automobile after acceleration, you can use the equation:
Final Speed = Initial Speed + (Acceleration × Time)
Given that the initial speed is 0 m/s and the acceleration is 3 m/s^2 (meters per second squared), and the time is 4 seconds, you can substitute these values into the equation:
Final Speed = 0 m/s + (3 m/s^2 × 4 s)
Final Speed = 0 m/s + 12 m/s
Final Speed = 12 m/s
So, your answer of 12 m/s is correct.
3. In this case, the automobile is already traveling at 30 km/hr (kilometers per hour) at time = 0. To calculate the distance traveled during the 2 seconds of acceleration, you need to first convert the initial speed from km/hr to m/s.
Given that 1 km/hr = 1000 m/3600 s, you can convert 30 km/hr to m/s using the formula:
Initial Speed (m/s) = Initial Speed (km/hr) × (1000 m/3600 s)
Initial Speed (m/s) = 30 km/hr × (1000 m/3600 s)
Initial Speed (m/s) ≈ 8.33 m/s (rounded to two decimal places)
Now, you can use the equation for distance traveled during constant acceleration:
Distance = Initial Speed × Time + (1/2) × Acceleration × Time^2
Substituting the given values:
Distance = 8.33 m/s × 2 s + (1/2) × 3 m/s^2 × (2 s)^2
Distance = 16.66 m + 3 m/s^2 × 4 s^2
Distance = 16.66 m + 12 m
Distance ≈ 28.66 m (rounded to two decimal places)
So, it appears that your answer of 12 m/s for the distance traveled is incorrect. The correct answer is approximately 28.66 m.
4. To find the new velocity of the automobile, you need to calculate the time it takes to cover the given distance of 100 meters during the acceleration phase.
You can use the equation for distance traveled during constant acceleration:
Distance = Initial Speed × Time + (1/2) × Acceleration × Time^2
Substituting the given values:
100 m = 30 km/hr × (1000 m/3600 s) × Time + (1/2) × 3 m/s^2 × Time^2
100 m ≈ 8.33 m/s × Time + 1.5 m/s^2 × Time^2
This equation is a quadratic equation in terms of Time. To solve for Time, you can rearrange the equation and solve using quadratic formula or factoring. Once you find the value of Time, you can substitute it into the equation for final velocity:
Final Velocity = Initial Velocity + Acceleration × Time
The units for the final velocity will be in m/s, so the answer of 6030 m/s you provided does not seem to be correct.