Question

A particle moves along the x-axis so that at any time t, measured in seconds, its position is given by s(t) = 4sin(t) - cos(2t), measured in feet. What is the acceleration of the particle at time t = 0 seconds?

Answer 1

The acceleration of the particle in any time will be the second derivative of s(t)=4sin t-cos 2t

1)We have to find the first derivative.
v(t)=velocitiy in ft/s
v(t)=ds/dt=4cos (t)+2sin (2t)

2)We have to find the second derivative of s(t)
a(t)= acceleration in ft/s²
a(t)=d²/d²t=-4sin (t)+4 cos(2t)

3) We find the acceleration of the particle at t=0
a(0)=-4sin 0 +4 cos(2*0)=0+4=4

Answer: the acceleration of the particle at time t=0 seconds would be:
4 ft/s²