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

3804 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

It is given that f(x)=(x^2 +9x)/((x-1)(x^2 +9)). (i) Express f(x) in partial fractions. (ii) Hence find the integral of f(x) with respect to x.


How do you find the derivative of arcsinx?


Find the general solution of y'' - 3y' + 2y = 2e^x


Prove ∑r^3 = 1/4 n^2(n+1)^2


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences