233k views
2 votes
Let the velocity of a particle be given by v(t) = 2t+a.(a) Find the number a such that the average value of v(t) on the interval [0,1] is -2.(b) Using v(t) from part (a), find the distance traveled by the particle during the time period from [0,4].

User Helt
by
8.2k points

1 Answer

2 votes

Answer:

The velocity is v(t) = 2*t + a

a) we want to find the average velocity betwen t = 0 and t = 1.

We can do this as:

Average = (v(1) + v(0))/2 = (2*1 + a + 2*0 + a)/2 = 1 + a

b) now we want to find the total distance traveled in the time lapse from t = 0 to t = 4.

For this we can see the integral:


d = \int\limits^4_0 {2*t + a} \, dt = 4^2 + a*4 - 0^2 - a*0 = 4^2 + a*4 = 16 + a^2

User Davehenry
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories