A child in a sled is moving with a speed of 4.0 m/s across an iced over pond.If the total mass of the sled-child system is 85.0 kg,what magnitude of the average force is required to bring the sled to rest in 10.0 s?
A)14 N
B)24 N
C)34 N
D)44 N
E)54 N

Question

Quizplus · Accepted Answer

To bring the sled to rest, we need to calculate the deceleration and then use Newton's second law to find the force. The initial velocity (v_i) is 4.0 m/s, and the final velocity (v_f) is 0 m/s (since the sled comes to rest), over a time (t) of 10.0 s. The deceleration (a) can be found using the formula $a = \frac{v_f - v_i}{t}$. Plugging in the values, $a = \frac{0 - 4.0}{10.0} = -0.4 \, m/s^2$. The negative sign indicates deceleration. The force required can be found using Newton's second law, $F = ma$, where $m$ is the mass and $a$ is the acceleration (or in this case, deceleration). The mass (m) is 85.0 kg, and the acceleration (a) is -0.4 m/s^2. Thus, $F = 85.0 \times -0.4 = -34 \, N$. The negative sign indicates the direction of the force is opposite to the motion, but since the question asks for the magnitude, we take the absolute value, which is 34 N.

A Child in a Sled Is Moving with a Speed