Please help me with this question

Question

A speedboat increases its speed uniformly from v_i = 20.0 m/s

 to v_f = 33.0 m/s

 in a distance of Δx = 2.00 ✕ 10² m.

(b) For the given information, what single equation is most appropriate for finding the acceleration?

v_f² = v_i² + 2a(Δx)

v_f = v_i + at

a = vf − vi

tf − ti

Δx = vit + 1

2

(c) Solve the equation selected in part (b) symbolically for the boat's acceleration in terms of v_f, v_i, and Δx.

a = 

 

 

(d) Substitute given values, obtaining the acceleration.

 

(e) Find the time it takes the boat to travel the given distance.

 

I know answers to A and B, I do not know the answers for C, D, or E if you please help me here

Answer 1

Obviously, since you are given v_i, v_f, and Δx and are trying to determine "a", you need an equation that has those 4 things in it and the one that works is:

v_f² = v_i² + 2a(Δx)

To solve this equation for "a", subtract v_i² from both sides to get:

v_f² - v_i² = 2a(Δx)

Then divide both sides by "2" and then by "Δx" to get:

(v_f² - v_i²)/(2Δx) = a

So a = (v_f² - v_i²)/(2Δx)

Substituting the values you get:

a = (33² - 20²)/(2•(2 x 10²))

a = (1089 - 400)/(2•200)

a = 689/400

a = 1.7225

It would be appropriate to round to 3 significant figures and, since you are using SI units, you can apply the SI unit of acceleration, which is m/s² to get:

a = 1.72 m/s²

To find the time, you must use another equation that has time in it. One that will work is:

v_f = v_i + at

Solving for "t" you get:

t = (v_f - v_i)/a

But you should use the entire value of "a" you calculated (a = 1.7225):

t = (33 - 20)/1.7225

t = 7.55 seconds