you started to run at 10km/h when you left your house and you arrived at school .5 hours later. assuming that your average acceleration was 30 /h2, how fast were you running when you arrived
To determine how fast you were running when you arrived at school, we can use the kinematic equation:
v = u + at
Where:
- v is the final velocity (the speed at which you arrived at school)
- u is the initial velocity (the speed at which you started running from your house)
- a is the acceleration
- t is the time interval
Given information:
- u = 10 km/h (initial velocity)
- t = 0.5 hours (time interval)
- a = 30 km/h^2 (acceleration)
First, convert the time interval from hours to seconds as the acceleration is given in km/h^2:
t = 0.5 hours * 3600 seconds/hour = 1800 seconds
Now, substitute the given values into the equation:
v = 10 km/h + 30 km/h^2 * 1800 seconds
To solve this, we need to ensure the units are consistent. Since we want to determine the speed in km/h, the resulting unit should be in km/h as well.
Since we have km/h^2 * seconds, let's convert the seconds to hours by dividing by 3600:
v = 10 km/h + 30 km/h^2 * (1800 seconds / 3600 seconds/hour)
v = 10 km/h + 30 km/h^2 * 0.5 hour
Now simplify:
v = 10 km/h + 15 km/h
v = 25 km/h
Therefore, you were running at a speed of 25 km/h when you arrived at school.