Calculate the distance travelled by a car with a velocity of 30m/s and it increase its speed to 60 m/s in 2 hours.assume acceleration is constant.
uniform acceleration means that the average speed is the numerical average of the initial speed and the final speed
average speed ... (30 + 60) / 2 = 45
60 s in a min ... 60 min in an hr
distance = 45 * 60 * 60 * 2 (meters)
40m/s
To calculate the distance traveled by the car, we need to determine the time taken for the car to accelerate from 30 m/s to 60 m/s.
We know that acceleration (a) is the rate of change of velocity (v) with respect to time (t). In this case, we want to find the time it takes for the car to accelerate from 30 m/s to 60 m/s.
The formula to calculate acceleration is:
a = (change in velocity) / (time taken)
a = (60 m/s - 30 m/s) / (time taken)
Given that the acceleration is constant, we can rearrange the formula to solve for time:
time taken = (change in velocity) / (acceleration)
time taken = (60 m/s - 30 m/s) / (acceleration)
Now, we need to determine the value of acceleration. Since we assume the acceleration is constant, we can use the formula:
acceleration = (change in velocity) / (time taken)
acceleration = (60 m/s - 30 m/s) / (2 hours)
Note: We need to convert the time taken from hours to seconds, as velocity is in meters per second.
Now we can substitute the known values into the formula:
acceleration = (60 m/s - 30 m/s) / (2 hours)
acceleration = (60 m/s - 30 m/s) / (2 hours * 3600 seconds/hour)
Simplifying:
acceleration = 30 m/s / (2 * 3600 s)
acceleration = 30 / 7200 m/s^2
acceleration = 0.0041667 m/s^2 (rounded to 4 decimal places)
Now that we know the acceleration, we can substitute it back into the time formula to find the time taken:
time taken = (60 m/s - 30 m/s) / (0.0041667 m/s^2)
time taken = 30 / 0.0041667 seconds
time taken ≈ 7200 seconds
Now, we have the time it took for the car to accelerate from 30 m/s to 60 m/s, which is 7200 seconds.
To calculate the distance traveled during this time, we can use the equation:
distance = initial velocity * time + 0.5 * acceleration * time^2
Since the car is already moving initially at 30 m/s, we substitute the values:
distance = 30 m/s * 7200 s + 0.5 * 0.0041667 m/s^2 * (7200 s)^2
Simplifying:
distance = 216000 m + 0.5 * 0.0041667 m/s^2 * 51840000 s^2
distance ≈ 216000 m + 108000 m
distance ≈ 324000 m
Therefore, the distance traveled by the car is approximately 324,000 meters.