Aparticle moves along the x-axis with velocity given by v(t)=3t2+6t for time tâ¥0. if the particle at position x=2 at time t=0, what is the position of the particle at time t=1?
a) 4
b) 6
c) 0
d) 11
e) 12

b) 6

Explanation:

Given

v(t)=3t²+6t

X(0) = 2

X(1) = ?

Knowing that

v(t)=3t²+6t = dX/dt

⇒ ∫dX = ∫(3t²+6t)dt

⇒ X - X₀ = t³ + 3t²

⇒ X(t) = X₀ + t³ + 3t²

If  X(0) = 2

⇒  X(0) = X₀ + (0)³ + 3(0)² = 2

⇒  X₀ = 2

then we have

X(t) = t³ + 3t² + 2

when

t = 1

X(1) = (1)³ + 3(1)² + 2

X(1) = 6

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

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this means that the temperature of both substances will be equal