1. ## Slopes of Secants

Flare is shot up with an upwards velocity of 30m/s
The height of the flare is given by:
$
h=-5t^{2}+30t+10
$

d) Determine the instantaneous velocity of the flare at t = 3 seconds by using the slopes of secants (1 mark for table, 2 marks for slopes)

I'm not really sure what I'm suppose to do, I know how to get slopes of secants but I dont have any secants..... Can someone just help explain the question....thanks

Flare is shot up with an upwards velocity of 30m/s
The height of the flare is given by:
$
h=-5t^{2}+30t+10
$

d) Determine the instantaneous velocity of the flare at t = 3 seconds by using the slopes of secants (1 mark for table, 2 marks for slopes)

I'm not really sure what I'm suppose to do, I know how to get slopes of secants but I dont have any secants..... Can someone just help explain the question....thanks
1. Choose two values of t such that t = 3 is the mean of them. For instance:

$t_1 = 2$
$t_2 = 4$

2. Now calculate h(2) = ... and h(4) = ...
Calculate the slope between $P_1(2, h(2))$ and $P_2(4, h(4))$. This slope has the same value as the instantaneous velocity at t = 3.

3. Remark: This method only works if you are dealing with parabolas

4. Try if you get the same result if you use
$t_1 = 0$
$t_2 = 6$

5. You should have got 0.