This question is incomplete, the complete question is;
Suppose that the position of a particle is given by s=f(t)=5t³ + 6 t+ 9.
(a) Find the velocity at time t.
(b) Find the velocity at time t=3 seconds
Answer:
a) the velocity at time t is ( 15t² + 6 ) m/s
b) Velocity at time t=3 seconds is 141 m/s
Explanation:
Give the data in the question;
position of a particle is given by;
s = f(t) = 5t³ + 6t + 9
Velocity at t;
we differentiate with respect to t
so
V(t) = f'(t) = d/dt ( 5t³ + 6t + 9 )
V(t) = f(t) = 5(3t²) + 6(1) + 0 )
V(t) = f(t) = ( 15t²+6 ) m/s
Therefore, the velocity at time t is 15t²+6 m/s
b) Velocity at t = 3 seconds
V(t) = f(t) = ( 15t²+6 ) m/s
we substitute
V(3) = ( 15(3)² + 6 ) m/s
V(3) = ( (15 × 9) + 6 ) m/s
V(3) = ( 135 + 6 ) m/s
V(3) = 141 m/s
Therefore, Velocity at time t=3 is 141 m/s
