Answer:
v = 220 m / s
Explanation:
This is a kinematics exercise, the expression for velocity is
v = 25 t² - 80 t - 200
asks the velocity for time t = 6 s.
let's calculate
v = 25 6² - 80 6 - 200
v = 220 m / s
The velocity for the first six seconds when acceleration is zero is -44 m/s.
The velocity of an object is the rate of change displacement with time.
The velocity of the object for the first six seconds when the acceleration is zero is calculated as follows;
[tex]a = \frac{dv}{dt} \\\\a = 50t - 80\\\\0 = 50t - 80\\\\50t = 80\\\\t = 1.6 \ s[/tex]
Velocity when time = 1.6 s
[tex]v(1.6) = 25(1.6)^2 - 80(1.6) - 200\\\\v(1.6) = -264 \ m/s[/tex]
The velocity for the first six seconds when acceleration is zero.
[tex]v = v_{a =0} + v_6\\\\v = - 264 \ + 25(6)^2 - 80(6) - 200\\\\v = -44 \ m/s[/tex]
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