Q. 50 - Calculus

Question

Stuart left his house at noon and walked north on Pine Street for $20$ minutes. At that point he realized he was late for an appointment at the dentist, whose office was located south of Stuart’s house on Pine Street; fearing he would be late, Stuart sprinted south on Pine Street, past his house, and on to the dentist’s office. When he got there, he found the office closed for lunch; he was $10$ minutes early for his $12:40$ appointment. Stuart waited at the office for $10$ minutes and then found out that his appointment was actually for the next day, so he walked back to his house. Sketch a graph that describes Stuart’s position over time. Then sketch a graph that describes Stuart’s velocity over time.

Step-by-Step Solution

Answer

Ans:   

    Graph of the position of person S is given below:

     Graph of the velocity function overtime is given below:

Step 1. Given information.

   According to the given situation Sketch graph 

1 >  graph position over time

2 >  graph velocity over time

Step 2. Consider a coordinate plane that has a position at the vertical axis and time at the horizontal axis.

The position of the person S at time $t=0$ is $0$ . As the time increases the person S moves towards north for $20$ minutes.

Consider the north direction indicates the position axis.

After $20$ minutes, the person moves towards the south which is indicated by the negative direction.

Person S moves $10$ minutes towards the south and rested for $10$ minutes then moves towards the north.

Step 3. Sketch the graph of the position of the person with the help of the above description.

Step 4. Given situation for velocity.

Consider the person S moves towards the north with the constant with for $20$ minutes. The speed in the direction of north is positive and the speed of person S in the direction of the south is negative.

Person S runs for $20$ minutes with constant speed then runs $10$ minutes in the direction of south which is considered as negative.

Graph the velocity function over time with the help of the above description.