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1 answer:
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Answer:
The value of the constant k is 2
Explanation:
We have the equation of the velocity = kt² , where k
is constant and t is the time in second
The particle's position at = 0 is
= -9 m
The particle's position at = 3 s is
= 9 m
We need to find the value of the constant k
The relation between the velocity and the displacement in a particular
time is x =
Remember in integration we add power by 1 and divide the expression
by the new power
→ x =
c is the constant of integration to find it substitute the initial value of x
and t in the equation of x
→ = 0 ,
= -9 m
→ -9 = k (0)³ + c
→ -9 = c
Substitute the value of c in the equation of x
→ x = k t³ - 9
To find k substitute the values of = 3 s ,
= 9 m
→ 9 = k (3)³ - 9
→ 9 = (27) k - 9
→ 9 = 9 k - 9
Add 9 to both sides
→ 18 = 9 k
Divide both sides by 9
→ k = 2
<em>The value of the constant k is 2</em>