Question

The speed of a block traveling on a horizontal frictional surface changes from \(v_i = 13 \ \text{m/s}\) to \(v_f = 12 \ \text{m/s}\) in a distance of \(d = 9.5 \ \text{m}\).

A. Determine the acceleration of the block.
B. Use the kinematic equation to find the time it takes to decelerate.
C. Calculate the force acting on the block.
D. Discuss the role of friction in the deceleration.

Answer 1

The block's deceleration is found using kinematic equations with the given velocity and distance. Time and force calculations follow, with friction playing the central role in the deceleration of the block.

Step-by-step explanation:

The student's question involves the deceleration of a block on a horizontal surface with friction and requires calculation of acceleration, time, and force. Given an initial velocity (vi) of 13 m/s and a final velocity (vf) of 12 m/s over a distance (d) of 9.5 m, we can use the kinematic equation vf2 = vi2 + 2ad to find the acceleration (a). Rearranging this for acceleration, we get a = (vf2 - vi2)/(2d), which yields a negative value indicating deceleration. To find the time (t) it takes to decelerate, we use vf = vi + at. Solving for t gives us the deceleration time.

To calculate the force (F) acting on the block, we use Newton's second law (F = ma). The role of friction in this scenario is to provide the force that opposes the motion of the block, causing it to decelerate. Since there are no other forces mentioned, we can deduce that the frictional force is responsible for the block's deceleration.