Find the displacement function if the acceleration function is a=2t+5. Assume a zero initial condition of displacement and v=8 when t=1.

MYTUTOR SUBJECT ANSWERS

Answers / Further Mathematics / A Level / Find the displacement function if the acceleration function is a=2t+5. Assume a zero initial condition of displacement and v=8 when t=1.

537 views

Find the displacement function if the acceleration function is a=2t+5. Assume a zero initial condition of displacement and v=8 when t=1.

Integrating the acceleration function gives the velocity function v, as below:
v = t² +5t +C₁, where C₁ is a constant.

Integrating the velocity function gives the displacement function x, as below:
x = t³/3 + 5t²/2 + C₁t + C₂, where C₂ is another constant.

The answer is completed by finding the 2 constants, C₁ and C₂.

With a zero initial condition of displacement, that means t=0, x=0. Put this initial condition into the displacement function ---> C₂ = 0.

The boundary condition is that: v=8 when t=1. Simply put this condition into the velocity function ---> C₁ = 2.

Thus, the complete displacement function is as below:
x = t³/3 + 5t²/2 + 2t

Justin H. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mathem...

1 year ago

Answered by Justin , an A Level Further Mathematics tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

102 SUBJECT SPECIALISTS

John W. A Level Maths tutor, GCSE Maths tutor

View profile

£20 /hr

John W.

Degree: Mathematics (Masters) - St. Andrews University

Subjects offered:Further Mathematics , Maths

“I've done a broad range of maths learning and tutoring over the years, now continuing this on to university I'm sure I'll be able to help you out! ”

1 completed tutorial

Save profile

Ayyub A. A Level Maths tutor, 13 Plus Maths tutor, 11 Plus Maths tut...

View profile

£24 /hr

Ayyub A.

Degree: Mathematics Msci (Bachelors) - Bristol University

Subjects offered:Further Mathematics , Maths+ 1 more

“Hi I'm Ayyub, current student at Bristol university studying Maths. I have significant tutoring experience in maths and hopefully i'll be able to help you out.”

5.0

47 reviews | 50 completed tutorials

Save profile

Jacob F. A Level Maths tutor, GCSE Maths tutor, A Level German tutor,...

View profile

£20 /hr

Jacob F.

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered:Further Mathematics , Maths+ 2 more

“2nd year Maths undergrad with enhanced DBS (CRB) certification and experience teaching in secondary schools and at University. Fluent German speaker.”

5.0

26 reviews | 30 completed tutorials

Save profile

See more A Level Further Mathematics tutors

About the author

View profile

£20 /hr

Justin H.

Degree: Mechanical Engineering (Masters) - Bristol University

Subjects offered:Further Mathematics , Physics+ 1 more

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

Save profile

Version:	3.46.1
Build:	38ba4033af73
Time:	2017-06-23T10:54:26Z

MYTUTOR SUBJECT ANSWERS

Find the displacement function if the acceleration function is a=2t+5. Assume a zero initial condition of displacement and v=8 when t=1.

Still stuck? Get one-to-one help from a personally interviewed subject specialist

102 SUBJECT SPECIALISTS

About the author

You may also like...

Posts by Justin

Other A Level Further Mathematics questions

One-to-one help is at your fingertips