Question

If a rock is thrown upward on the planet Mars with a velocity of 10 mys, its height in meters t seconds later is given by y=10t-1.86t².

Find the average velocity over the given time intervals:
(i) [1, 2]
(ii) [1, 1.5]
(iii) [1, 1.1]
(iv) [1, 1.01]
(v) [1, 1.001]

Answer 1

The average velocity of a rock thrown on Mars is calculated using the position-time function for various time intervals to illustrate the approach toward instantaneous velocity.

Step-by-step explanation:

The average velocity of a rock thrown upward on Mars is calculated over various time intervals using the given equation y=10t-1.86t². To find the average velocity, we use the formula Average velocity = (y final - y initial) / (t final - t initial).

For interval [1, 2], we first calculate the positions y at t=1 and t=2 using the equation and then find the average velocity. We repeat this process for each interval given: [1, 1.5], [1, 1.1], [1, 1.01], and [1, 1.001]. As the intervals get smaller, the average velocity approaches the instantaneous velocity at t=1 second. This concept demonstrates the relationship between average velocity and instantaneous velocity, defining the notion of a derivative in calculus.