Question

answer the following

1. a car traveled 150 km in 3 hours. what is the speed of the car?
2. a boy runs 400 meters in 80 seconds. what is his speed?
3. a boy travels 40km north in 1.5 hours. what is his velocity?
4. a lorry drives 20km north, then 20km south. completing the trip in 1 hour.

a. what is the total distance traveled?
b. what is the displacement?
c. what is the average speed?

Explanation:

Step1: Recall the speed formula

Speed \(v=\frac{d}{t}\), where \(d\) is distance and \(t\) is time.

Step2: Solve problem 1

For the car, \(d = 150\) km and \(t=3\) hours. Then \(v=\frac{150}{3}=50\) km/h.

Step3: Solve problem 2

For the boy, \(d = 400\) meters and \(t = 80\) seconds. Then \(v=\frac{400}{80}=5\) m/s.

Step4: Recall the velocity formula

Velocity \(v=\frac{\Delta x}{t}\), where \(\Delta x\) is displacement.

Step5: Solve problem 3

For the boy, \(\Delta x = 60\) km north and \(t = 1.5\) hours. Then \(v=\frac{60}{1.5}=40\) km/h north.

Step6: Solve problem 4a

Total distance \(D\): The taxi travels \(20\) km north and \(20\) km south. \(D=20 + 20=40\) km.

Step7: Solve problem 4b

Displacement \(\Delta X\): The taxi starts and ends at the same place. \(\Delta X=0\) km.

Step8: Solve problem 4c

Average speed \(v_{avg}=\frac{D}{t}\). Assume the time for each part of the trip: if we assume the speed is constant for each part (say speed \(v_1 = v_2\)), and using \(t=\frac{d}{v}\). But if we just use the total - distance formula \(v_{avg}=\frac{40}{t_{total}}\). If we assume the speed for each part is \(v\) (say \(v = 20\) km/h for each part, \(t_1=\frac{20}{20}=1\) h and \(t_2=\frac{20}{20}=1\) h, \(t_{total}=2\) h). Then \(v_{avg}=\frac{40}{2}=20\) km/h.

Answer:

1. \(50\) km/h
2. \(5\) m/s
3. \(40\) km/h north

4a. \(40\) km
4b. \(0\) km
4c. \(20\) km/h