Aceleration of a particle

Question

. A particle moves on a line away from its initial position so that after t seconds its distance is s = 3t^2 +t meters from its initial position.

(a) At what time does the particle have a velocity of 30 m/s

Answer 1

Our goal is to find the time at which the particle reaches a velocity of 30 m/s.

In order to solve this problem, we need to get an equation for velocity in terms of time, v(t). Because the distance equation, s(t), is given to us, we can solve for v(t) by taking the derivative of s(t).

s^'(t) = v(t) = 6t + 1

Now we have the velocity of the particle in terms of t. Now, we have to find the time at which the particle is moving at a velocity of 30 m/s. To do this, set v(t) equal to 30 m/s, and solve for time!

v(t) = 6t + 1

30 = 6t + 1

29 = 6t

t = (29/6) seconds

≈ 4.83 seconds