Question

a speed boat increase in speed uniformly from 20 m/s to 30 m/s over a distance of 200m. What is the acceleration of the boat

Answer 1

The acceleration of the boat is 1 m/s².

Step-by-step explanation:

To find the acceleration of the boat, we can use the formula for acceleration:

Acceleration = (Change in velocity) / (Change in time)

In this case, the boat's initial velocity is 20 m/s and the final velocity is 30 m/s. The change in velocity is 30 m/s - 20 m/s = 10 m/s.

The boat covers a distance of 200 m, so we can calculate the time taken:

Time = (Distance) / (Velocity) = 200 m / 20 m/s = 10 s

Now we can substitute the values into the formula for acceleration:

Acceleration = (Change in velocity) / (Change in time) = 10 m/s / 10 s = 1 m/s²

Answer 2

The speed boat's acceleration is calculated using the kinematic equation vf2 = vi2 + 2ad. Substituting the given values results in an acceleration of 1.25 m/s2.

Step-by-step explanation:

Calculating Acceleration

To calculate the acceleration of the speed boat, we will use the kinematic equation that relates initial velocity (vi), final velocity (vf), acceleration (a), and distance (d):

vf2 = vi2 + 2ad

We know the initial velocity (vi) is 20 m/s, the final velocity (vf) is 30 m/s, and the distance covered (d) is 200 m. Plugging these values into the equation gives us:

302 = 202 + 2 · a · 200

900 = 400 + 400a

a = · (900 - 400) / 400

a = 1.25 m/s2

Therefore, the acceleration of the boat is 1.25 m/s2.