The velocity function of a moving particle on a coordinate line is v(t) = 3 cos(2t) for 0 is less than or equal to t and t is greater than or equal to 2pi (c) Determine the total distance travelled by the particle during 0 is less than or equal to t is greater than or equal to 2pi.
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write5,348 answers
starTop subjects are Math, Science, and Business
You need to remember that the total distance may be found using the absolute value function such that:
`|cos 2t| = cos 2t, 2t in (0,pi/2)U((3pi)/2,2pi)`
`|cos 2t| = - cos 2t, 2t in (pi/2,(3pi)/2)`
You need to evaluate the following definite integrals to find the total distance, such that:
`d = int_0^(pi/2) (3-cos2t) dt + int_(pi/2)^((3pi)/2) (3+cos2t) dt + int_((3pi)/2)^(2pi) (3-cos2t) dt`
Using the fundamental theorem of calculus yields:
`d = (3t-(sin2t)/2)|_0^(pi/2) + (3t+(sin2t)/2)_(pi/2)^((3pi)/2) + (3t-(sin2t)/2)|_((3pi)/2)^(2pi)`
`d = (3pi/2) - (sin pi)/2 - 0 + 0 + (9pi/2) + (sin3pi)/2 - (3pi)/2 - (sin pi)/2 + 6pi - (sin 4pi)/2 - (9pi/2) + (sin3pi)/2`
`d = 6pi`
Hence, evaluating the total distance travelled by the moving particle yields `d = 6pi.`
Related Questions
- The velocity function of a moving particle on a coordinate line is v(t) = 3cos(2t) for 0 is less...
- 1 Educator Answer
- Find the position of the particle. a(t) = 2t + 3, s(0) = 8, v(0) = −3A particle is moving with...
- 1 Educator Answer
- The velocity function of a moving particle on a coordinate line is v(t) = 3 cos(2t) for 0 is...
- 1 Educator Answer
- The velocity function of a moving particle on a coordinate line is v(t) = 3 cos(2t) for 0 is...
- 1 Educator Answer
- The velocity function of a moving particle on a coordinate line is v(t) = 3 cos(2t) for 0 is less...
- 1 Educator Answer