Question

1. a cyclist rides 20 km north in 2 hours, then 10 km south in 1 hour. find the total displacement and average velocity.
2. a runner completes a 400 m track in 50 seconds. what is the average speed?
3. a person walks 3 km east in 1 hour and then 4 km north in 2 hours. find the total distance and the magnitude of the displacement.

Explanation:

Problem 5

Step1: Define Displacement Direction

Let north be positive. Displacement \( d_1 = +20\) km, \( d_2 = -10\) km (south is negative).

Step2: Calculate Total Displacement

Total displacement \( D = d_1 + d_2 = 20 + (-10) = 10\) km (north).

Step3: Calculate Total Time

Total time \( t = 2 + 1 = 3\) hours.

Step4: Calculate Average Velocity

Average velocity \( v = \frac{D}{t} = \frac{10}{3} \approx 3.33\) km/h (north).

Step1: Recall Average Speed Formula

Average speed \( s = \frac{\text{total distance}}{\text{total time}}\).

Step2: Identify Distance and Time

Distance \( d = 400\) m, time \( t = 50\) s.

Step3: Calculate Average Speed

\( s = \frac{400}{50} = 8\) m/s.

Step1: Calculate Total Distance

Total distance \( d = 3 + 4 = 7\) km.

Step2: Calculate Displacement Magnitude

Displacement is the hypotenuse of a right triangle (east and north are perpendicular). Using Pythagoras: \( D = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\) km.

Answer:

Total displacement: \( 10\) km north; Average velocity: \(\frac{10}{3} \approx 3.33\) km/h north.

Problem 6