Question

A projectile is released with an initial (vertical) velocity of 95 m/s. Use the formula v(t) = 95 − 9.8t for velocity to determine the distance traveled during the first 14 s. (Round your answer to two decimal places.)

Answer 1

Answer:

$s = 369.6\ m$

Explanation:

given,

v(t) = 95 − 9.8 t

time, t= 14 s

velocity is the change in distance of an object in the given interval of time.

$\dfrac{ds}{dt}=95-9.8 t$

$ds = (95 - 9.8 t)dt$

integrating both side

$\int ds = \int (95-9.8 t)dt$

$s = 95 t-9.8\dfrac{t^2}{2}$

now,

Distance traveled by the object in 14 s

t = 14

$s = 95\times 14-9.8\dfrac{14^2}{2}$

$s = 369.6\ m$

Distance traveled by the object is equal to 369.6 m