A particle moves along the x-axis so that at time t≥0, its velocity is given by v(t) = sint + cost. What is the acceleration at the time when the velocity is first equal to 0?

Question

How would you solve it without using a calculator?

A) -√ 2

B) -1

C) 1

D) √ 2

Answer 1

Acceleration is the first derivative of velocity with respect to time

v = sin t + cos t

v' = cos t - sin t

v'(0)= cos (0) -sin(0) = 1 - 0 =1

Zero is a special angle which you should know without a calculator