Friday

November 28, 2014

November 28, 2014

Posted by **Jane** on Sunday, March 29, 2009 at 11:24pm.

A particle moves on the x-axis 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**, Monday, March 30, 2009 at 4:04amv = 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**, Thursday, October 27, 2011 at 4:44amDamon is wrong. The acceleration equation would be 2te^-t - 4e^-t.

**Answer this Question**

**Related Questions**

Calculus (Answer Check) - A particle moves along the x-axis so that its velocity...

Calculus (Answer Check) - A particle moves along the x-axis so that its ...

Calculus (Answer Check) - Are my answers right? If they are wrong you dont have ...

math - a particle starts at time t = 0 and moves along the x - axis so that its ...

Ap calc - A particle moves on the x axis so that it's position at any time t is ...

Calculus - An ant moves along the x-axis with velocity given by v(t)=tsin(t^2), ...

Calc - A particle moves along the x-axis in such a way that it's position in ...

Calc - A particle moves along the x-axis in such a way that it's position in ...

Calculus-particle motion - 1. A particle is moving on the x-axis (or any number ...

calculus - a particle moves along the y axis so that its position at any time t...