Answer:
43 m/s
Explanation:
Mass, m = 5 kg
Force, F(t) = 6t² - 4t + 3
To find the speed, we first need to get the acceleration, a.
Force is the product of mass and acceleration. It is given as:
F = ma
Therefore, acceleration is:
a(t) = F(t)/m
a(t) = (6t² - 4t + 3) / 5
a(t) = 1.2t² - 0.8t + 0.6
Acceleration is the differentiation of velocity with respect to time, t. Therefore, to get velocity, v, we integrate a(t):
a(t) = dv(t) / dt
=> v(t) = (1.2/3)t³ - (0.8/2)t² + 0.6t
v(t) = 0.4t³ - 0.4t² + 0.6t
Therefore, at time t = 5secs, velocity is:
v(5) = 0.4 * (5³) - 0.4 * (5²) + 0.6 * 5
v(5) = 50 - 10 + 3
v(5) = 43 m/s
The velocity at time, t = 5 secs is 43 m/s
