A 100-kg object moves on a level surface with a coefficient of friction of 0.40.If the initial velocity is 15 m/s,how long will it take for it to come to rest?
A)1.5 s
B)3.8 s
C)6.7 s
D)37.5 s

Question

Quizplus · Accepted Answer

To find the time it takes for the object to come to rest, we first calculate the force of friction acting on it, which is given by $F_{friction} = \mu \times m \times g$, where $\mu$ is the coefficient of friction, $m$ is the mass of the object, and $g$ is the acceleration due to gravity (approximately $9.8 \, m/s^2$). For a 100-kg object with a coefficient of friction of 0.40, the force of friction is $F_{friction} = 0.40 \times 100 \, kg \times 9.8 \, m/s^2 = 392 \, N$.This frictional force acts as the decelerating force, so we can use Newton's second law to find the deceleration $a = F/m$, which gives us $a = 392 \, N / 100 \, kg = 3.92 \, m/s^2$.To find the time it takes for the object to come to rest, we use the equation $v = u + at$, where $v$ is the final velocity (0 m/s for coming to rest), $u$ is the initial velocity (15 m/s), and $a$ is the deceleration (-3.92 m/s^2, negative because it's deceleration). Rearranging for $t$, we get $t = (v - u) / a = (0 - 15) / -3.92 = 3.83 \, s$, which rounds to approximately 3.8 seconds.

A 100-Kg Object Moves on a Level Surface with a Coefficient