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

JH
Answered by Justin H. Further Mathematics tutor

3670 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

A line has Cartesian equations x−p = (y+2)/q = 3−z and a plane has equation r ∙ [1,−1,−2] = −3. In the case where the angle θ between the line and the plane satisfies sin⁡θ=1/√6 and the line intersects the plane at z = 0. Find p and q.


Let A, B and C be nxn matrices such that A=BC-CB. Show that the trace of A (denoted Tr(A)) is 0, where the trace of an nxn matrix is defined as the sum of the entries along the leading diagonal.


Convert the general complex number z=x+iy to modulus-argument form.


a) Find the general solution to the differential equation: f(x)=y''-12y'-13y=8. b) Given that when x=0, y=0 and y'=1, find the particular solution to f(x).


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences