Question

You and a friend are driving to the beach during spring break. You travel 14.5 km east and then 66.5 km south in a total time of 50 minutes. (a) What is the average speed of the trip? (b) What is the magnitude of the average velocity? -In this question for part B, why isnt it necessay to find the unit vectors for displacement?

Answer 1

(a). The average speed is 97.23 km/hr.

(b). The average velocity is 81.70 km/min.

Step-by-step explanation:

Given that,

Distance in east = 14.5 km

Distance in south = 66.5 km

Time = 50 min = 0.833 hr

(a). We need to calculate the average speed

Using formula of average speed

`v_(avg)=(D)/(T)`

Where, D = total distance

T = total time

Put the value into the formula

`v_(avg)=(14.5+66.5)/(0.833)`

`v_(avg)=97.23\ Km/hr`

(b). We need to calculate the displacement

Using Pythagorean theorem

`d=\sqrt{(d_(e))^2+(d_(s))^2}`

Put the value into the formula

`d=√((14.5)^2+(66.5)^2)`

`d=68.06\ km`

(b). We need to calculate the average velocity

Using formula of average velocity

`v_(avg)=(d)/(t)`

Where, d = displacement

t = time

Put the value into the formula

`v_(avg)=(68.06)/(0.833)`

`v_(avg)=81.70\ km/min`

Here, We can not necessary to find the unit vectors for displacement because we need to the displacement for find the average velocity.

Hence, (a). The average speed is 97.23 km/hr.

(b). The average velocity is 81.70 km/hr.