Question

Derek launches a puck across a sheet of ice. the puck has an initial velocity of 12 m/s in the positive direction. the puck has a constant rate of acceleration of − 0.40 m/s². after 6.5 seconds, what is the puck’s displacement?

a. 61 meters
b. − 8.5 meters
c. 78 meters
d. 70 meters

Answer 1

The displacement of the puck after 6.5 seconds is found using the kinematic formula for displacement, resulting in a value of 70 meters. Option D is correct.

Step-by-step explanation:

The question asks for the displacement of a hockey puck that has been launched across ice with an initial velocity and a constant negative acceleration, after a given period of time. Using the formula of kinematic motion for displacement (s = ut + 1/2 at2), where u is the initial velocity, a is the acceleration, and t is the time, we can calculate the puck's displacement.

Here, u = 12 m/s, a = -0.40 m/s2, and t = 6.5 seconds.

First, let's compute the displacement using the given values:

s = (12 m/s)(6.5 s) + 0.5(-0.40 m/s2)(6.5 s)2

Calculating the values step by step:

s = 78 m + 0.5(-0.40 m/s2)(42.25 s2)

s = 78 m - 0.5(16.9 m)

s = 78 m - 8.45 m

s = 69.55 m

Considering the options provided, the closest numerical value to 69.55 m is rounded to 70 meters. Therefore, the correct answer for the displacement of the puck is 70 meters.