Question

Dan bikes 10 km west and then bikes another 5 km west. What is dans velocity if it takes 45 minutes

Answer 1

Dan's velocity is calculated by dividing his total displacement of 15 km west by the total time of 45 minutes, which is equivalent to 0.75 hours, hence his velocity is 20 km/h west.

Step-by-step explanation:

The student asks about Dan's velocity after biking 10 km west and then another 5 km west in a total time of 45 minutes. To find the average velocity, we need to calculate the total displacement over the total time. Since Dan's travel direction is consistent (west), the total displacement is simply the sum of the two distances. So, his displacement is 10 km + 5 km = 15 km west. To get the velocity, we divide the displacement by the time in hours. First, we convert 45 minutes into hours by dividing by 60, which gives us 0.75 hours. Hence, Dan's velocity is 15 km / 0.75 h = 20 km/h west.

Answer 2

he velocity vector is found by taking the displacement divided by the amount of time.

The total displacement is 15 km West.

So the velocity is 15 km W / 45 min.

To convert to km/hr, multiply by 60 min/ 1 hour so the minutes will cancel in the numerator and denominator

15 * 60 / 45 km W / hr = 20 km/h West.

Also sometimes the term "velocity" is used when "speed" is intended in which case you can forget about what direction the movement was in and just say the speed was 20 km/hour.

Also if you want to keep the direction and use vectors, you might have a coordinate system with the x axis going in the East direction, the y axis in the North direction, and assume the world is flat :-) Then if the unit vector for x is "i" and the unit vector for y is "j" then you're looking at a velocity vector that is -20 i (in km/hour).