HS Calculus
posted by Jane .
Having trouble with this questions. Please help.
A particle moves on the xaxis so that its position at any time t (is greater than or equal to) 0 is given by x(t) = 2te^t
a) Find the acceleration of the particle at t=0
b)find the velocity of the particle when its acceleration is 0.
c) find the total distance traveled by the particle from t=0 to t=5

HS Calculus 
Damon
v = dx/dt = 2 t (e^t) + 2 e^t
a = d^2x/dt^2 = 2 t e^t + 2 e^t  2 e^t = 2 t e^t
so
a) at t = 0, a = 2(0) e^0 = 0
b) v(0) = 0 + 2 (1) = 2
c) Does the particle turn around and head back between t = 0 and t = 5?
v = 0 = 2 t e^t +2 e^t
t = 1 when the sign of v reverses
when t = 1, x = 2 e^1 = .736
so from t = 0 to t = 1 it went .736 positive
now from t = 1 to t = 5
x(5) = 10 e^10
= tiny
so it came back essentially to zero
so total distance = .736 forward + .736 in reverse = 1.47 
HS Calculus 
Marcos
Damon is wrong. The acceleration equation would be 2te^t  4e^t.
Respond to this Question
Similar Questions

Calculus (Answer Check)
Are my answers right? If they are wrong you don't have to tell me how to do it its okay =) A particle starts at time t=0 and moves along the xaxis so that its position at any time t(greater or equal to) 0 is given by x(t)=(t1)^3 
Calculus (Answer Check)
A particle moves along the xaxis so that its velocity at time t, 0(less than or equal)t(greater or equal to)5 is given by v(t)=3(t1)(t3). at time t=2 the position of the particle is x(2)=0. 1. find the minimum acceleration of the … 
Calculus (Answer Check)
A particle moves along the xaxis so that its velocity at time t, 0(less than or equal)t(greater or equal to)5 is given by v(t)=3(t1)(t3). at time t=2 the position of the particle is x(2)=0. 1. find the minimum acceleration of the … 
Calculus
An ant moves along the xaxis with velocity given by v(t)=tsin(t^2), t is greater than or equal to zero. Given that x(t) is the position of the particle at time t and that x(0)=3, find x(2) Find the total distance traveled by the particle … 
Ap calc
A particle moves on the x axis so that it's position at any time t is greater than or equal to 0 is given by x(t)=2te^t. A) find velocity for any t is greater or equal to 0 
calculus
5. A particle moves along the y – axis with velocity given by v(t)=tsine(t^2) for t>=0 . a. In which direction (up or down) is the particle moving at time t = 1.5? 
math
a particle starts at time t = 0 and moves along the x  axis so that its position at any time t is greater than or equal to zero is given x(t) = (t1)^3(2t3) A. Find the velocity of the particle at any time t greater than or equal … 
Calc
A particle moves along the xaxis in such a way that it's position in time t for t is greator or equal to 0 is given by x= 1/3t^3  3t^2 +8 A) show that at time t= 0 the particle is moving to the right. B) find all values of t for … 
Calc
A particle moves along the xaxis in such a way that it's position in time t for t is greator or equal to 0 is given by x= 1/3t^3  3t^2 +8 A) show that at time t= 0 the particle is moving to the right. B) find all values of t for … 
Calculus
A particle moves along the xaxis and its position for time t is greater than or equal to 0, is s (t)=cos(2t)+sec(t). When t=pi, the acceleration of the particle is