Question
Asked Nov 11, 2019
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Find the position at the time t= 2 seconds of a particle if v(t)= 5t-3; s= 3 when t= 0.

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Expert Answer

Step 1

Given:

Velocity of a particle at time t as v(t)= 5t - 3
Also, given that when t 0, position of particle 's' is 3.
To find: Position of the particle at time t 2
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Velocity of a particle at time t as v(t)= 5t - 3 Also, given that when t 0, position of particle 's' is 3. To find: Position of the particle at time t 2

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Step 2

We know that, velocity is change in displacement to time.

ds
V =
dt
ds
5t 3
dt
(5t 3)dt ds
Now, integrating both sides,
(5t- 3)dt ds
5t2
3t sc
2
5t2
3t c s
2
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ds V = dt ds 5t 3 dt (5t 3)dt ds Now, integrating both sides, (5t- 3)dt ds 5t2 3t sc 2 5t2 3t c s 2

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Step 3

We use the condition giv...

5(0)2
- 3(0) - c = 3
2
c 3
Substituting the value of c,
5t2
s(t)
2
3t3
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5(0)2 - 3(0) - c = 3 2 c 3 Substituting the value of c, 5t2 s(t) 2 3t3

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Tagged in

Math

Calculus

Integration