Q. 46 - Precalculus Enhanced with Graphing Utilities

Question

The following sketch represents the speed v (in miles per hour) of Michael’s car as a function of time t (in minutes). 

(a) Over what interval of time was Michael traveling fastest? 

(b) Over what interval(s) of time was Michael’s speed zero? 

(c) What was Michael’s speed between 0 and 2 minutes? 

(d) What was Michael’s speed between 4.2 and 6 minutes? 

(e) What was Michael’s speed between 7 and 7.4 minutes? 

(f) When was Michael’s speed constant? 

Step-by-Step Solution

Answer

(a) $(7-7.4)$

(b) $0, 9.1, (4.2-6)$

(c) Increasing from 0 mph to 30 mph

(d) 0 mph

(e) 50 mph

(f) $(2-2),(4.2-6),(7-7.4),(7.6-8)$

Part (a )Step 1. Given information

We have been given a sketch that sketch represents the speed v (in miles per hour) of Michael’s car as a function of time t (in minutes).  

We have to find over what interval of time was Michael traveling fastest.

Part (a) step 2. Find the greatest value of V(t) from the graph

The greatest value of speed is 50.

Therefore, over the interval of $(7-7.4)$ Michael was traveling fastest.

Part (b) Step 1. Find the interval where V(t) is zero.

Speed is zero where V(t) is zero on the graph.

Therefore,  over the interval of $(4.2-6)$ and at t = 0 and t = 9.1 Michael's speed was zero.

Part (c) Step 1. Observe the interval ( 0 , 2 ) .

Michael’s speed was increasing from 0 miles per hour to 30 miles per hour between 0 and 2 minutes.

Part (d) Step 1. Observe the interval ( 4 . 2 - 6 ) .

Michael’s speed was 0 miles per hour between 4.2 and 6 minutes 

Part (e) Step 1. Observe the interval ( 7 , 7 . 4 ) .

Michael’s speed was 50 miles per hour between 7 and 7.4 minutes.

Part (f) Step 1. Find the intervals where the graph is a horizontal line

The graph is a horizontal line over four intervals.

Therefore, Michael’s speed was constant over the intervals:

$(2-2),(4.2-6),(7-7.4),(7.6-8)$