Answer:
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
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4.266 m is the radius of the circular path the electron follows.
Given
Speed of electron (v) = 7.5 × 10⁶ m/s
Earth's Magnetic Field (B) = 1 × 10⁻⁵ T
We already know that
Mass of electron (m) = 9.1 × 10⁻³¹ kg
Charge on electron (q) = 1.6 × 10⁻¹⁹ C
According to the formula
Radius of circular path(r) = mass on electron × speed/ Charge × Magnetic field
Radius of circular path(r) = m × v/q × B
Put the values into the formula
r = 9.1 × 10⁻³¹ × 7.5 × 10⁶/ 1.6 × 10⁻¹⁹ × 10⁻⁵
On solving, we get
r = 4.266 m
Hence, 4.266 m is the radius of the circular path the electron follows.
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