Question

A particle moves with a uniform velocity function V = 4 ¾ - 3t. calculate the maximum distance traveled by the particle before stopping.

Answer 1

The velocity is

$$V = 4 \frac{3}{4} - 3t = 3 - 3t = 3(1-t)$$

so the particle stops at time t=1. To calculate the distance we integrate

$$l= \int^1_0 v(t) dt= 3\int^t_0 (1-t) dt = 3 \bigg(t - \frac{t^2}{2}\bigg)\bigg|^{t=1}_{t=0} = 3\bigg(1 - \frac{1}{2}\bigg) = \frac{3}{2}$$