To calculate the distance an automobile moves while its speed increases uniformly from 15 kph to 45 kph in 20 seconds, we can use the equation for average velocity:
Average velocity = (final velocity + initial velocity) / 2
The average velocity can also be expressed as the total distance traveled divided by the time taken:
Average velocity = distance / time
Rearranging this equation, we get:
Distance = Average velocity * time
First, let's convert the speeds from kilometers per hour (kph) to meters per second (m/s) since the time is given in seconds.
15 kph = 15 * (1000/3600) m/s ≈ 4.17 m/s 45 kph = 45 * (1000/3600) m/s ≈ 12.50 m/s
Now we can calculate the distance traveled:
Average velocity = (4.17 m/s + 12.50 m/s) / 2 ≈ 8.34 m/s
Distance = Average velocity * time Distance = 8.34 m/s * 20 s Distance ≈ 166.8 meters
Therefore, the automobile moves approximately 166.8 meters while its speed increases uniformly from 15 kph to 45 kph in 20 seconds.