Question

A boat travels 12.0m while it reduces its velocity from 9.5m/s to 5.5 m/s. What is the magnitude of the boat acceleration while it travels the 12.0 m?

a) 1.3 m/s2
b) 3.0 m/s2
c) 2.5 m/s²
d) 7.5 m/s2​

Answer 1

The magnitude of the boat's acceleration while it travels 12.0 m is found using a kinematic equation, resulting in an acceleration of 2.5 m/s^2. This value is calculated by inserting the given velocities and displacement into the rearranged equation, and taking the absolute value of the negative result to determine the magnitude.

Step-by-step explanation:

To calculate the magnitude of the boat's acceleration while it travels the 12.0 m, we can use the kinematic equation that relates initial velocity (v_i), final velocity (v_f), acceleration (a), and displacement (s):

v_f^2 = v_i^2 + 2as

Rearranging the equation to solve for a, we get:

a = (v_f^2 - v_i^2) / (2s)

Plugging the values:

Initial velocity, v_i = 9.5 m/s

Final velocity, v_f = 5.5 m/s

Displacement, s = 12.0 m

a = ((5.5 m/s)^2 - (9.5 m/s)^2) / (2*12.0 m)

a = (30.25 - 90.25) / 24

a = (-60) / 24

a = -2.5 m/s^2

Since acceleration is a vector quantity and we are interested in its magnitude, we take the absolute value and ignore the negative sign. Therefore, the magnitude of the boat's acceleration while it travels the 12.0 m is 2.5 m/s^2, which matches option (c).