Question

please give exact answers

Question 6 (1 point)

Problems 6-9 use the following information. A dog frolics rectilinearly with acceleration a(t) = 2sin(t) + 9e^3t + 3t² + 5 m/s². Initial position and velocity are both 0. At t = 0.8 s:

What is the dog's acceleration (m/s²)? Answer with 3 significant figures.

Question 7 (1 point)

What is the dog's velocity (m/s)? Answer with 3 significant figures.

Question 8 (1 point)

What is the dog's position (m)? Answer with 3 significant figures.

Question 9 (1 point)

Does the dog ever backtrack?

Question 9 options:

	Yes, at t = π, 3π, 5π ... etc. seconds
	Yes, at t = π/2, 3π/2, 5π/2 ... etc. seconds
	Yes, at t = 0.8 s
	No

Question 10 (1 point)

Given acceleration a(s) = 2 + 7cos(s) m/s² where initial position is 0 and initial velocity is 2 m/s, what is velocity (m/s) at s = 4π m? Answer with 3 significant figures.

Answer 1

a=2sin(t) +9e^3t+3t^{_​​​​​​​​​2}+5

At t=0.8s

a= 2sin(0.8) +9e^3×0.8+3×0.8²+5

a=107.56m/s²

Since a=dv/dt hence integration of acceleration gives velocity

v=2 (-cos(t)) +3e^3t+t³+5t

v=2(-cos(0.8)) +3e^3×0.8+0.8³+5×0.8

V=36.19m/s