Homework Help: math

Posted by Dave on Monday, February 23, 2009 at 6:41pm.

The acceleration of a particle at a time t moving along the x-axis is give by: a(t) = 4e^(2t). At the instant when t=0, the particle is at the point x=2, moving with velocity v(t)=-2. Find the position of the particle at t=1/2

if you could show me how to get that please

math - bobpursley, Monday, February 23, 2009 at 6:50pm
postition= integral v dt
v= int a dt
find v first, you know the constant of integration from at t=2

Then integrate again to get position.
math - Reiny, Monday, February 23, 2009 at 6:55pm
a(t) = 4e^(2t)
so v(t) = 2e^(2t) + C (I integrated, since dv/dt = a)
when t=0, v=-2
-2 = 2e^0 + c
c = -4 and then
v)t) = 2e^(2t) - 4
since ds/dt = v
s = e^(2t) - 4t + k
when t=0, s=2 (I assume that is what you meant by x=2)
2 = e^0 - 4(0) + k
k = 1
then s(t) = e^(2t) - 4t + 1
s(1/2) = e^1 - 2 + 1
= e - 1

Answer this Question

Related Questions

Calculus - a particle starts at time t = 0 and moves along the x axis so that ...
physics - The position of a particle moving along an x axis is given by x = 15t2...
math - a particle starts at time t = 0 and moves along the x - axis so that its ...
Calculus - At time t >or= to 0, the position of a particle moving along ...
Physics - A particle is initially moving along the positive x-axis at a speed of...
physics - 1.Give examples of a one-dimensional motion where (a) the particle ...
Calculus (Answer Check) - Are my answers right? If they are wrong you dont have ...
Calculus - The velocity of a particle moving along the x-axis is given by f(t)=6...
Physics-Help please... - The graph give the acceleration a versus time t for a ...
calculus - 5. A particle moves along the y – axis with velocity given by v(...

For Further Reading

First Name:
School Subject:
Answer: