Question

The height ‘h’ in metres of a ball above the ground can be modelled by the function h(t) = -5t² + 20 t, where t is the time in seconds. Use difference quotient to determine approximately the instantaneous speed at t = 2 sec.

Answer 1

To find the approximate instantaneous speed at t = 2 s, we can use the difference quotient.

Step-by-step explanation:

The height of the ball above the ground can be modeled by the function h(t) = -5t² + 20t, where t is the time in seconds. To find the approximate instantaneous speed at t = 2 s, we can use the difference quotient. The instantaneous speed is given by the derivative of the function, which is h'(t) = -10t + 20.

Using the difference quotient formula, we have:

h'(2) = lim(h → 0) [h(t+2) - h(t)] / h

By plugging in the values, we get:

h'(2) = (-5(2+h)² + 20(2+h) - (-5(2)² + 20(2))) / h

After simplifying, we can take the limit as h approaches 0 to find the approximate instantaneous speed at t = 2 s.