Question

connection the motion of a person or object can be explained by mining how the position changes over time. practice using the ematical model, average speed equation. 1. a truck driver makes a trip that covers 2,380 km in 28 hours. what is the drivers average speed in km/h? 2. what is the average speed of a soccer ball that travels 34 m in 2 s? 3. how long would it take a bus traveling at 52 km/h to travel 130 km? three - dimensional thinking isaiah leaves one city at noon. he has to be at another city 186 km away at 3:00 p.m. the speed limit the entire way is 65 km/h. can he arrive at the second city on time? explain your reasoning using mathematical evidence.

Explanation:

Step1: Recall average speed formula

Average speed: $v = \frac{d}{t}$

Step2: Solve Q1: Truck speed

Substitute $d=2380$ km, $t=28$ h
$v = \frac{2380}{28} = 85$ km/h

Step3: Solve Q2: Soccer ball speed

Substitute $d=34$ m, $t=2$ s
$v = \frac{34}{2} = 17$ m/s

Step4: Solve Q3: Bus travel time

Rearrange formula: $t = \frac{d}{v}$
Substitute $d=130$ km, $v=52$ km/h
$t = \frac{130}{52} = 2.5$ hours

Step5: Solve Q4: Isaiah's arrival check

First, calculate available time: $t=3$ hours (noon to 3:00 PM)
Calculate max distance at speed limit: $d = v \times t = 65 \times 3 = 195$ km
Compare to required 186 km: $195 > 186$

Answer:

1. 85 km/h
2. 17 m/s
3. 2.5 hours
4. Yes, he can arrive on time. At the maximum allowed speed of 65 km/h, he can travel 195 km in 3 hours, which is more than the 186 km needed to reach the second city.