Question

solution
find the mass of the system from the definition of weight, w = mg.
find the acceleration of the system from the second law.
use kinematics to find the distance moved in 2.00 s, with v0 = 0.
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remarks note that the constant applied force of 20.0 n is assumed to act on the system at all times during its motion. if the force were removed at some instant, the system would continue to move with constant velocity and hence zero acceleration. the rollers have an effect that was neglected here.
question if the weight of the crate were doubled, the acceleration would be multiplied by
and the displacement attained in 2.0 s would be multiplied by

Explanation:

Step1: Recall relevant formulas

Weight formula $w = mg$, Newton - second law $F=ma$ and kinematic formula $\Delta x=\frac{1}{2}at^{2}$ (with $v_0 = 0$).

Step2: Analyze the change in mass when weight is doubled

If $w$ is doubled, since $w = mg$ and $g$ is constant, $m$ is also doubled. From $a=\frac{F}{m}$, with $F$ constant, when $m$ is doubled, $a$ is halved ($a'=\frac{F}{2m}=\frac{1}{2}\times\frac{F}{m}$).

Step3: Analyze the change in displacement

From $\Delta x=\frac{1}{2}at^{2}$, with $t$ constant, and $a$ halved, $\Delta x$ is halved ($\Delta x'=\frac{1}{2}a't^{2}=\frac{1}{2}\times\frac{1}{2}at^{2}$).

Answer:

$\frac{1}{2}$; $\frac{1}{2}$