Step-by-step explanation:
The displacement of a particle d (in km) as a function of time t (in hours) is given by :
[tex]d=2t^3+5t^2-3[/tex]
Displacement at t = 4 hours,
[tex]d(4)=2(4)^3+5(4)^2-3=205\ km[/tex]
Velocity of particle is given by :
[tex]v=\dfrac{dd}{dt}\\\\v=\dfrac{d(2t^3+5t^2-3)}{dt}\\\\v=6t^2+10t[/tex]
Velocity at t = 4 hours,
[tex]v=6(4)^2+10(4)=136\ km/h[/tex]
Acceleration of the particle is given by :
[tex]a=\dfrac{dv}{dt}\\\\a=\dfrac{d(6t^2+10t)}{dt}\\\\a=12t+10[/tex]
At t = 4 hours,
[tex]a=12(4)+10=58\ km/h^2[/tex]
Therefore, the displacement, velocity and acceleration at t = 4 hours is 205 km, 136 km/h and 58 km/h² respectively.
