Respuesta :
Answer:
The total distance traveled by the particle is S = 30.
Step-by-step explanation:
Given that velocity,
v(t) = 2t + 1
To find the total distance travel, we integrate the velocity function, v(t), to obtain the distance function s(t), and evaluate the resulting distance at the interval given. That is at t = 0 to t = 5.
Integrating v(t) with respect to t, we have
s(t) = t² + t + C.
At t = 5
s(5) = 5² + 5 + C
= 25 + 5 + C
= 30 + C
At t = 0
S(0) = 0 + 0 + C
= C
The required distance is now
S(5) - S(0)
= 30 + C - C
= 30.
The total distance travelled by the particle in metres between time t = 0 secs and t = 5 secs is; 30
We are given the velocity function as;
v (t) = 2t + 1
Now, to find distance we will simply integrate the velocity function.
Thus;
S(t) = ∫v (t)
Thus;
S(t) = ∫2t + 1
S(t) = t² + t + c
Where x is a constant variable
Now, we want to find the total distance between times t = 0 seconds and t = 5 seconds.
Thus;
Total distance = S(5) - S(0)
Total distance = (5² + 5 + c) - (0² + 0 + c)
Total distance = 30 metres
Read more about integral of velocity at; https://brainly.com/question/24516698
