On-line Math 21

2.4  Applications of the derivative.

Example 1 If the position of a particle (in meters, along a line) is given by s = t³-4.5t²-7t , for t ³ 0 , find the velocity v(t) , and find when the velocity reaches 5 m/sec . What motion did the particle have at t = 0 ?

Solution:

The velocity is v(t) = 3t²-9t-7 , so, at t = 0 the velocity was -7 , meaning that the particle was going backwards at 7 m/sec . The velocity was 5 when

5 = 3t2-9t-7, or 0 = 3t2-9t-12 = (3t+12)(t-1).

Now, we presume that time is going forward, so we will not count the solution t = -4 , so the answer will be t = 1 only.

Copyright (c) 2000 by David L. Johnson.