Suppose the distance $s$ (in feet) covered by a car moving along a straight road after $t$ sec is given by the function $s = f ( t ) = 3 t ^ { 2 } + 13 t$. Calculate the (instantaneous) velocity of the car when $t = 35$.
A) 223 ft/sec
B) 16 ft/sec
C) 560 ft/sec
D) 4130 ft/sec

Question

Quizplus · Accepted Answer

The velocity of the car is given by the derivative of the distance function with respect to time:

$$v = \frac{ds}{dt} = f'(t) = 6t + 13$$

To find the instantaneous velocity at $t = 35$, we substitute $t = 35$ into the derivative:

$$v = 6(35) + 13 = 223$$

Therefore, the answer is choice A, 223 ft/sec.

Suppose the Distance sss (In Feet) Covered by a Car Moving Along a Straight

Suppose the Distance $s$ (In Feet) Covered by a Car Moving Along a Straight