S = 6t² + 3t + 7, 0 ≤ t ≤ 2 Find the body's displacement and average velocity for the given time interval. A) 30 m, 30 m/sec B) 44 m, 22 m/s C) 18 m / sec , 27 m /sec D) 30 m / sec , 15 m /sec

30m, 24m/s

Step-by-step explanation:

Given the expression for the position of the object expressed as:

S = 6t² + 3t + 7,

At t = 0

S0 = 6(0)²+3(0)+7

S0 = 0+0+7

S(0) = 7m

At t = 2

S2 = 6(2)² + 3(2)+ 7

S2 = 6(4)+6+7

S2 = 24+13

S2 = 37

The displacement = S2-S0 = 37-7= 30m

For the velocity

V = dS/dt = 12t+3

At t = 0

V0 = 12(0)+3

V0 = 3

At t= 2

V2 = 12(2)+3

V2 = 24+3

V2 =27

The velocity will be V2-V0 = 27-3 = 24m/s