Question

If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height, in meters, t seconds later, is given by the equation y=10t−1.86t². Find the average velocity over the time interval [1,3].

Answer 1

Approximately
`2.56\; {\rm m\cdot s^(-1)}` (assuming that height is measured in meters.)

Step-by-step explanation:

The velocity of an object is the rate of change in the position. To find the average velocity, divide the change in position (displacement) by the length of the time interval.

In this question:

• At
  `t = 3`, position of the rock was
  `10\, (3) - 1.86\, (3^(2)) = 13.26` (meters.)
• At
  `t = 1`, position of the rock was
  `10\, (1) - 1.86\, (1^(2)) = 8.14` (meters.)

In other words, position of the rock has changed from
`8.14\; {\rm m}` to
`13.26\; {\rm m}`. The position of the rock has changed by
`\Delta x = 13.26\; {\rm m} - 8.14\; {\rm m} = 5.12\; {\rm m}`.

Divide this change in position by the duration of the time interval
`\Delta t = (3 - 1)\; {\rm s} = 2\; {\rm s}` to find the average velocity of the rock:

`\begin{aligned}& (\text{average velocity}) \\ =\; & \frac{(\text{change in position})}{(\text{change in time})} \\ =\; & (\Delta x)/(\Delta t) \\ =\; & \frac{5.12\; {\rm m}}{2\; {\rm s}} \\ =\; & 2.56\; {\rm m\cdot s^(-1)}\end{aligned}`.