Physics

Problem

A crate rests on a smooth warehouse floor. The following horizontal forces act on it at different times along the same straight line. • From

t = 0\,\text{s}

t = 4\,\text{s}

40\,\text{N}

to the east and

25\,\text{N}

to the west. • From

t = 4\,\text{s}

t = 8\,\text{s}

: an additional force of

15\,\text{N}

to the west is applied while the original forces continue unchanged. • After

t = 8\,\text{s}

: all external horizontal forces are removed. (a) For each of the three time intervals (

0

–

4\,\text{s}

4

–

8\,\text{s}

, and after

8\,\text{s}

) identify the direction of the net force acting on the crate. (b) For each interval, describe qualitatively how the velocity of the crate changes (increases, decreases, remains constant) and give a brief reason based on Newton’s First Law. (c) Sketch a possible qualitative velocity–time graph for the entire motion from

t = 0\,\text{s}

to a short time after

t = 8\,\text{s}

. Label key features clearly.

Intuitive explanation

This problem teaches you how net force determines acceleration, and how that acceleration changes the velocity over time. The key insight is to find the net force in each interval by adding forces as vectors (east positive, west negative), then use Newton's Second Law to predict whether velocity increases, decreases, or stays constant. Once you know the acceleration in each phase, you can sketch how velocity evolves—the slope of the $v$ – $t$ graph tells you the acceleration in that interval.

Intuitive explanation

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