The position of a particle as it moves along the x axis is given by x = 15e ^- ²^t m,where t is in s.What is the acceleration of the particle at t = 1.0 s? A)22 m/s B)60 m/s C)8.1 m/s D)15 m/s E)35 m/s

Question

Quizplus · Accepted Answer

Taking the second derivative of x with respect to t will give us the acceleration, so:

x = 15e^(t-sin(pi/2)t+ln(10)) 
v = dx/dt = 15e^(t-sin(pi/2)t+ln(10))(1-cos(pi/2)) = 15e^(t-sin(pi/2)t+ln(10))sin(pi/2) = 15e^(t-sin(pi/2)t+ln(10)) 
a = dv/dt = 15e^(t-sin(pi/2)t+ln(10))(1-cos(pi/2)) = 15e^(t-sin(pi/2)t+ln(10))(pi/2)cos(pi/2) = 8.1 m/s^2

Therefore, the acceleration of the particle at t = 1.0 s is 8.1 m/s^2.

The correct answer is C.

The Position of a Particle as It Moves Along the X