Need help with two questions related to derivatives!

Question

1.An arrow is shot upward from the edge of a cliff such that its height h (in m) above the ground at time t (where t >= 0) is given by h = -4.9t^2 + 40t + 45 , where t is the time in seconds. Find its acceleration a.

Answer : -9.8m/s

Is this simply just a "trick question" or is there anything we can do to prove that the acceleration relates to the acceleration of gravity which is 9.8m/s^2?

2.An electron moves in an electric field according to the equation s = 10t^2 / t+1 , where s is in metres and t is in seconds. Find the velocity and acceleration of the electron when t = 5 seconds.

Answers: v = 9.72 m/s ; a = 0.0926 m/s^2

By differentiating the equation and substituting 5 I'm able to get 9.72 which is the velocity, but I do not understand why s' is the velocity and I do not know how to get the acceleration.

Answer 1

h(t) = -4.9t² + 40t + 45

Do the first derivative.

h'(t) = -9.8t + 40

Then the second derivative.

h''(t) = -9.8 → The acceleration due to gravity is -9.8 m/s².

s(t) = 10t² / t+1

s'(t) = 20t(t + 1) - 1(10t²)/ (t + 1)² = 10t² + 20t / t² + 2t + 1

s'(5) = [100(6) - 250] / 36 = 9.72 m/s

s''(t) = (20t +20)(t² + 2t + 1) - (2t + 2)(10t² + 20t)/ (t² + 2t + 1)²

s''(5) = (120)(36) - (12)(350) / (1296) = 0.0926 m/s²

Do the first derivative to find the velocity. Do the second derivative from there to find the acceleration.