At time t≥0 the acceleration of a particle that is moving along the x-axis is a(t)=t+2sin(t). At t=0 the velocity of the particle is -4. For what value of t

Question

At time t≥0 the acceleration of a particle that is moving along the x-axis is a(t)=t+2sin(t). At t=0 the velocity of the particle is -4. For what value of t will the velocity of the particle be zero?

Answer 1

a(t) = t + 2sin(t)

 

v(t) = ∫a(t)dt = t²/2 - 2cos(t) + c

 

v(0) = -4 ⇒

 

-2 + c = -4

 

c = -2

 

v(t) = t²/2 - 2cos(t) - 2

 

Set v(t) = 0 and solve for t.  

 

t²/2 - 2cos(t) - 2 = 0

 

This gives a transcendental equation, which you may need to solve numerically or graphically.  I suggest plotting this on a graphing calculator, and noting positive values of t when the curve crosses the t-axis.