Question

If a rock is thrown upward on the planet Mars with a velocity of 11 m/s, its height (in meters) after t seconds is given by H = 11t − 1.86t².

Find the velocity of the rock when t = a.

Answer 1

To calculate the rock's velocity at time t = a on Mars, differentiate the height function H(t) and substitute a into the resulting velocity function.

Step-by-step explanation:

To find the velocity of the rock thrown upward on Mars at time t = a, we need to differentiate the given height function with respect to time.

The height function given is H = 11t − 1.86t². The derivative of H with respect to t provides the velocity function: V(t) = dH/dt = 11 − (2 × 1.86t).

To find the velocity at t = a, we simply plug in a into the velocity function: V(a) = 11 − (2 × 1.86a). This is the rock's velocity at time t = a on Mars.