application\n3. a hockey puck of mass 200 g slides along the ice with a speed of 1.2 m/s when it reaches a…

Explanation:

Step1: Convert mass to kg

Mass ( m = 200\ g = 0.2\ kg ).

Step2: Find frictional force

Frictional force ( f = \mu N ), normal force ( N = mg ) (since vertical forces balance), so ( f = \mu mg ). Substituting values: ( f = 0.25\times0.2\times9.8 = 0.49\ N ).

Step3: Find acceleration (deceleration)

From Newton's second law ( F = ma ), here ( F = f ) (deceleration), so ( a = \frac{f}{m} = \frac{0.49}{0.2} = -2.45\ m/s^2 ) (negative for deceleration).

Step4: Use kinematic equation ( v = v_0 + at )

Final velocity ( v = 0 ), initial velocity ( v_0 = 1.2\ m/s ), acceleration ( a = -2.45\ m/s^2 ). Solving for ( t ): ( 0 = 1.2 - 2.45t ), so ( t = \frac{1.2}{2.45} \approx 0.49\ s ). (Free - body diagram: Forces on puck - gravitational force ( mg ) downward, normal force ( N ) upward (balanced), frictional force ( f ) opposite to motion (horizontal).)

Answer:

The time taken for the puck to stop is approximately (\boldsymbol{0.49\ s}) (and the free - body diagram shows gravitational force downward, normal force upward, and frictional force opposite to motion).