For the position function f(t) (feet) find the instantaneous velocity at time seconds.
A) feet per second
B) feet per second
C) feet per second
D) feet per second

Question

For the position function f(t)  (feet) find the instantaneous velocity at time  seconds.
A) feet per second 
B) feet per second 
C) feet per second 
D) feet per second

Quizplus · Accepted Answer

To find the instantaneous velocity, we need to take the derivative of the position function with respect to time.

f(t) = 11e^(aa948_cdcb_b47a_84bc_1dae4e972d60_TB2342_11)

f'(t) = 11e^(aa948_cdcb_b47a_84bc_1dae4e972d60_TB2342_11) * (aa948_cdcb_b47a_84bc_1dae4e972d60_TB2342_11)

We can now substitute the given time value (11eaa948_cdcb_db8b_84bc_7788a4b8e115_TB2342_11 seconds) into the derivative to find the instantaneous velocity at that time:

f'(11eaa948_cdcb_db8b_84bc_7788a4b8e115_TB2342_11) = 11e^(aa948_cdcb_b47a_84bc_1dae4e972d60_TB2342_11) * (aa948_cdcb_b47a_84bc_1dae4e972d60_TB2342_11)

The answer has been given in scientific notation, so we can use the same notation to simplify:

f'(11eaa948_cdcb_db8b_84bc_7788a4b8e115_TB2342_11) = 1.1 x 10^(aa948_cdcb_b47a_84bc_1dae4e972d60_TB2342_11+1) * (aa948_cdcb_b47a_84bc_1dae4e972d60_TB2342_11)

f'(11eaa948_cdcb_db8b_84bc_7788a4b8e115_TB2342_11) = 1.1 x 10^(aa948_cdcb_b47a_84bc_1dae4e972d60_TB2342_11+1+aa948_cdcb_db8e_84bc_354b2cd5938e_TB2342_11) feet per second

Simplifying further, we can add the exponents:

f'(11eaa948_cdcb_db8b_84bc_7788a4b8e115_TB2342_11) = 1.1 x 10^(aa948_cdcb_b47a_84bc_1dae4e972d60_TB2342_11+aa948_cdcb_db8f_84bc_b7d32b095ab1_TB2342_11) feet per second

Therefore, the correct answer is choice C, 11eaa948_cdcb_db8e_84bc_354b2cd5938e_TB2342_11 feet per second.

For the Position Function F(t) (Feet) Find the Instantaneous