Respuesta :
Answer:
v=206ft/s , a=120ft/s
Step-by-step explanation:
We are given the equation of displacement
[tex]S = 6t^3 + 6t^2 + 8t + 3,[/tex]
- velocity = ds/dt
upon differentiating the given equation
ds/dt = [tex]18t^2 + 12t + 8[/tex]
upon substituting t = 3
v = 206ft/s
- Acceleration
a= dv/dt
upon differentiating
dv/dt = 36t + 12
put t= 3
a=120ft/s
The velocity at the given time is 206 ft/sec and the acceleration is [tex]\rm 120\;ft/sec^2[/tex] and this can be determined by using the differentiation method.
Given :
[tex]\rm s = 6t^3+6t^2+8t+3[/tex]
The following steps can be used in order to determine the velocity and acceleration at the given time:
Step 1 - In order to determine the velocity, differentiate the given function of displacement with respect to time 't'.
[tex]\rm v = \dfrac{ds}{dt} = 18t^2+12t+8[/tex] --- (1)
Step 2 - Now, substitute the value of 't' in the above function.
[tex]\rm v = 18\times (3)^2+12\times 3+8[/tex]
v = 206 ft/sec
Step 3 - Now, again differentiate the expression (1) in order to determine the acceleration.
[tex]\rm a = \dfrac{dv}{dt} = 36t+12[/tex]
Step 4 - Now, substitute the value of 't' in the above function.
[tex]\rm a = 36\times 3+12[/tex]
[tex]\rm a = 120\;ft/sec^2[/tex]
Therefore, the correct option is D).
For more information, refer to the link given below:
https://brainly.com/question/12134554
