Answer:
(a). a = -4309105 m/s
(b). t = 7.158 × 10 ⁻⁴ sec
Explanation:
from the question, given that;
initial speed (Vo) = 1340ft/s
x = 5 in = 0.4167 ft (conversion factor)
but V = (Vo - Kx)
where a = V dv/dx
∴ a = (Vo-Kx) d/dx (Vo-Kx)
a = (Vo-Kx) (-K)│x=o
a = -KVo
therefore, 0 = 1340 - K (0.4167)
K = 1340/ 0.4167 = 3215.75 sec⁻¹
a = - 3215.75 × 1340
which gives a = -4309105 m/s
(b). given that x = 4.5 in = 0.375 ft
V = dx/dt = V₀ - Kx
= [tex]\int\limit^{0.375} _0 {(1/1340 - 3215.75x)} dx = \int\limits^t_0 {} \, dt[/tex]
= - 1/3215.75 [tex]\lim_{0 \to \00.375} (1340-3215.75x)[/tex]
t = 7.158 × 10 ⁻⁴ sec
