Answer:
Step-by-step explanation:
To solve this problem, we can use the equations of motion for a charged particle in an electric field. The equation we'll use is:
y = y₀ + v₀yt + 0.5at²
Where:
- y is the displacement of the particle after time t.
- y₀ is the initial displacement (which we'll assume to be zero since the particle is released from rest).
- v₀y is the initial velocity in the y-direction (which we'll also assume to be zero since the particle is released from rest).
- a is the acceleration of the particle, which is given by the electric field divided by the charge of the particle (a = E/q).
- t is the time.
Given:
- Particle charge (q) = +15.2 μC = +15.2 × 10⁻⁶ C
- Particle mass (m) = 1.58 × 10⁻⁵ kg
- Electric field (E) = +386 N/C
- Time (t) = 2.87 × 10⁻² s
First, let's calculate the acceleration (a):
a = E/q
a = 386 N/C / 15.2 × 10⁻⁶ C
a = 2.55 × 10⁴ m/s²
Now, we can calculate the displacement (y):
y = 0 + 0 + 0.5at²
y = 0.5 × (2.55 × 10⁴ m/s²) × (2.87 × 10⁻² s)²
y ≈ 10.5 m
Therefore, the displacement of the particle after a time of 2.87 × 10⁻² s is approximately 10.5 meters.