Question

A speed boat increases its speed uniformly from vi = 20.0 m/s to vf = 30.0 m/s in a distance of 2.00 x 10²m.

A) For the given information, what single equatino is most appropriate for finding the acceleration? (B) Solve the equation selected in part
B) symbolically for t he boats acceleration in terms of vf, va, and Δx.
C) Substitute given values, obtaining that acceleration.
D) Find the time it takes the boat to travel the given distance?

Answer 1

To find the acceleration of the speed boat, we can use the equation for average acceleration: a = (vf - vi) / Δx. By substituting the given values, we can find the acceleration. Then, using the equation Δx = vi x Δt + 1/2aΔt², we can solve for the time it takes for the boat to travel the given distance.

Step-by-step explanation:

The equation that is most appropriate for finding the acceleration is the equation for average acceleration:

average acceleration (a) = change in velocity (Δv) / change in time (Δt)

To solve this equation symbolically for the boat's acceleration (a), we can use the given values:

vf = final velocity = 30.0 m/s

vi = initial velocity = 20.0 m/s

Δx = change in distance = 2.00 x 10² m

Substituting these values into the equation, we have:

a = (vf - vi) / Δx

Now we can substitute the given values to find the acceleration:

a = (30.0 m/s - 20.0 m/s) / 2.00 x 10² m

Simplifying the equation gives:

a = 10.0 m/s / 2.00 x 10² m

Finally, we can calculate the time it takes for the boat to travel the given distance:

Using the equation for average acceleration, Δx = vi x Δt + 1/2aΔt², we can rearrange the equation to solve for Δt:

Δt = (√(vf - vi)² + 2aΔx) / a

Substituting the given values, we get:

Δt = (√(30.0 m/s - 20.0 m/s)² + 2(10.0 m/s²)(2.00 x 10² m)) / 10.0 m/s²

Simplifying the equation gives the time it takes for the boat to travel the given distance.