Question
Asked Dec 10, 2019
22 views
(2) The velocity function, in feet per second, is given for a particle moving in a straight line. Find
(a) the displacement and
(b) the total distance that the particle travels over the given interval
V (t) = 3t – 12,
0st<10
help_outline

Image Transcriptionclose

(2) The velocity function, in feet per second, is given for a particle moving in a straight line. Find (a) the displacement and (b) the total distance that the particle travels over the given interval V (t) = 3t – 12, 0st<10

fullscreen
check_circle

Expert Answer

Step 1

Displacement ‘D’ of a particle moving from point ‘a’ to point ‘b’ in a straight line with velocity ‘v’ is given by the formula. Using these values given to find displacement ‘D.

help_outline

Image Transcriptionclose

D=[v(}it a = 0 b= 10 10 D = | (3t – 12)dt

fullscreen
Step 2

Solving for displacement ‘D’ using basic definite integration.

help_outline

Image Transcriptionclose

312 D = – 12t 10 3(10) 3(0) - 12(10)– 2 +12(0) 2 = 150 – 120–0+0 = 30 feet ||

fullscreen
Step 3

Distance ‘S’ travelled by a particle form point ‘a’ to point ‘b’ in a straight ...

help_outline

Image Transcriptionclose

8 = j•O\« v(1 )dt a = 0 b=10 4 10 -v(t)dt+ S = 4

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Integration

Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A
add