质点在流体中作直线运动，受与速度成正比的阻力kv(k为常数)作用，t=0时质点的速度为v₀<br /> 证明<br /> (1) t时刻的速度为<img src="https://nimg.ppkao.com/2019-04/liyunao/2019041515512688455.jpg?sign=8f86d41bce783e578bd6095af8eae4ae&t=62d5df3b" /><br /> (2) 由0到的时间内经过的距离为<img src="https://nimg.ppkao.com/2019-04/liyunao/2019041515513738732.jpg?sign=d016b102b6222fefd846c8f1af161926&t=62d5df3b" /><br /> (3)停止运动前经过的距离为<img src="https://nimg.ppkao.com/2019-04/liyunao/2019041515514286.jpg?sign=299cdaa546a5cc7923c71f3de3b57e4e&t=62d5df3b" /><br /> <img src="https://nimg.ppkao.com/2019-04/liyunao/2019041515515039239.jpg?sign=cd5f63c8c0792ecc3a2a93856f0de2f7&t=62d5df3b" />