Question

A boat increases its speed from 5.0 m/ s to 7.5 m/ s over a distance of 50.0m. What is the boats acceleration?

Answer 1

v = 5 + a t
d = 5 t + (1/2) a t^2
so
50 = 5t + .5 a t^2
7.5 = 5 + a t
t = (7.5 - 5) / a = 2.5 / a
so
50 = 5 (2.5/a) +.5 a (6.25/a^2 )= 12.5/a + 3.13 /a = 15.6/a
a = 15.6/50
looks like we agree

Answer 2

To calculate the boat's acceleration, we can use the equation:

Acceleration = (final velocity - initial velocity) / time

However, we are not given the time taken to change the velocity, so we need to use a different equation:

Acceleration = (final velocity^2 - initial velocity^2) / (2 * distance)

Given:
Initial velocity (u) = 5.0 m/s
Final velocity (v) = 7.5 m/s
Distance (d) = 50.0 m

Plugging these values into the equation, we get:

Acceleration = (7.5^2 - 5.0^2) / (2 * 50.0)
Acceleration = (56.25 - 25) / 100
Acceleration = 31.25 / 100
Acceleration = 0.3125 m/s²

Therefore, the boat's acceleration is 0.3125 m/s².

Answer 3

Yes, it seems like we agree. The boat's acceleration is approximately 0.312 m/s².