Answer: Acceleration of the car at time = 10 sec is 108 [tex]m/s^{2}[/tex] and velocity of the car at time t = 10 sec is 918.34 m/s.
Explanation:
The expression used will be as follows.
[tex]M\frac{dv}{dt} = u\frac{dM}{dt}[/tex]
[tex]\int_{t_{o}}^{t_{f}} \frac{dv}{dt} dt = u\int_{t_{o}}^{t_{f}} \frac{1}{M} \frac{dM}{dt} dt[/tex]
= [tex]u\int_{M_{o}}^{M_{f}} \frac{dM}{M}[/tex]
[tex]v_{f} - v_{o} = u ln \frac{M_{f}}{M_{o}}[/tex]
[tex]v_{o} = 0[/tex]
As, [tex]v_{f} = u ln (\frac{M_{f}}{M_{o}})[/tex]
u = -2900 m/s
[tex]M_{f} = M_{o} - m \times t_{f}[/tex]
= [tex]2500 kg + 1000 kg - 95 kg \times t_{f}s[/tex]
= [tex](3500 - 95t_{f})s[/tex]
[tex]v_{f} = -2900 ln(\frac{3500 - 95 t_{f}}{3500}) m/s[/tex]
Also, we know that
a = [tex]\frac{dv_{f}}{dt_{f}} = \frac{u}{M} \frac{dM}{dt}[/tex]
= [tex]\frac{u}{3500 - 95 t} \times (-95) m/s^{2}[/tex]
= [tex]\frac{95 \times 2900}{3500 - 95t} m/s^{2}[/tex]
At t = 10 sec,
[tex]v_{f}[/tex] = 918.34 m/s
and, a = 108 [tex]m/s^{2}[/tex]
