Scarlett received the following problem:
A particle moves in a straight line with velocity $v(t)=2 t+5$ meters per second, where $t$ is time in seconds. At $t=1$, the particle's distance from the starting point was 5 meters in the positive direction. What is the particle's displacement between $t=1$ to $t=3$ seconds?

Which expression should Scarlett use to solve the problem?
Choose 1 answer:
(A) $\int_{1}^{3} v(t) d t+5$
(B) $\int_{1}^{3} v(t) d t$
(C) $v(3)-v(1)$
(D) $v^{\prime}(3)+5$

Question

Scarlett received the following problem:
A particle moves in a straight line with velocity $v(t)=2 t+5$ meters per second, where $t$ is time in seconds. At $t=1$, the particle's distance from the starting point was 5 meters in the positive direction. What is the particle's displacement between $t=1$ to $t=3$ seconds?

Which expression should Scarlett use to solve the problem?
Choose 1 answer:
(A) $\int_{1}^{3} v(t) d t+5$
(B) $\int_{1}^{3} v(t) d t$
(C) $v(3)-v(1)$
(D) $v^{\prime}(3)+5$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the particle's displacement between $t=1$ and $t=3$ seconds, we need to integrate the velocity function $v(t)=2t+5$ over the interval from $t=1$ to $t=3$. ‖ ‖ step 2 ⋮ The integral of the velocity function will give us the change in position, or displacement, from $t=1$ to $t=3$. ‖ ‖ step 3 ⋮ The displacement is given by the definite integral $\int_{1}^{3} v(t) dt$. ‖ ‖ step 4 ⋮ Since the particle's distance from the starting point at $t=1$ was 5 meters, we add this initial distance to the result of the integral to find the total displacement. ‖ ‖ step 5 ⋮ Therefore, the expression Scarlett should use to solve the problem is $\int_{1}^{3} v(t) dt + 5$. ‖ ∻Answer∻ ⚹ (A) $\int_{1}^{3} v(t) dt+5$ ⚹ ∻Key Concept∻ ⚹Displacement from Velocity Function⚹ ∻Explanation∻ ⚹The displacement of a particle is found by integrating its velocity function over the given time interval and adding the initial position if provided.⚹◊What is the formula for displacement in terms of velocity over an interval of time?⍭ Generate me a similar question◊

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