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 still cant get this one right. i think im not doing the formula right
First of all, 30 km/hr = 30,000 m/3600 s = 8.333 m/s
At the end of the 2 second interval, the speed is 6 m/s higher, or 14.333 m/s.
The average speed during the 2 second interval is 11.333 m/s.
Multiply that by 2.0 s for the distance travelled.
To determine the distance traveled by the automobile during the given time interval, we can use the following formula:
distance = initial velocity × time + (1/2) × acceleration × time^2
Let's break down the problem step by step:
Step 1: Convert the initial velocity from km/h to m/s.
The initial velocity is given as 30 km/hr. To convert it to m/s, divide by 3.6 since there are 3.6 meters in one kilometer.
Initial velocity = 30 km/hr ÷ 3.6 = 8.33 m/s (rounded to two decimal places).
Step 2: Calculate the distance traveled during the initial velocity phase.
We have the initial velocity and the time during which this velocity is maintained, which is 0-2 seconds. For this phase, we can use the formula d = v × t (distance equals velocity multiplied by time).
Distance during initial velocity phase = initial velocity × time = 8.33 m/s × 2 s = 16.67 meters (rounded to two decimal places).
Step 3: Calculate the distance traveled during the acceleration phase.
We know the acceleration is 3 m/s^2 and the time of acceleration is 2 seconds. Using the formula distance = (1/2) × acceleration × time^2, we can calculate the distance traveled during this phase.
Distance during acceleration phase = (1/2) × acceleration × time^2 = (1/2) × 3 m/s^2 × (2 s)^2 = 6 meters.
Step 4: Calculate the total distance traveled.
To find the total distance, we need to sum the distances calculated in Step 2 and Step 3.
Total distance = distance during initial velocity phase + distance during acceleration phase = 16.67 meters + 6 meters = 22.67 meters (rounded to two decimal places).
Therefore, the automobile travels a distance of approximately 22.67 meters during the 2-second time interval.