Detailed Solution
1. 1. Velocity: ∫₀ᵛ dv = ∫₀ᵗ 2t dt ⇒ v(t) = t². At t = 3 s, v = 3² = 9 m/s.
2. Displacement: ∫₀ˣ dx = ∫₀ᵗ t² dt ⇒ x(t) = t³ / 3. At t = 3 s, x = 3³ / 3 = 9 m.
HC Verma Ch 3 Q45 Masterclass: a(t) = 2t
v(t) = t² | x(t) = t³ / 3 | At t = 3s: v = 9m/s, x = 9m
Integration Ladder:
a = 2t ⇒ v = ∫ 2t dt = t² ⇒ x = ∫ t² dt = t³ / 3
At t = 3.0s: v = 9.0 m/s, x = 9.0 m
Time (t)
0.00 s
Position x(t)
0.00 m
Velocity v(t)
0.00 m/s
Accel a(t)
0.00 m/s²
1D CUBIC ACCELERATION TRACK
● Particle
→ Velocity v = t²
→ Accel a = 2t
VELOCITY v(t) = t² (PARABOLA)
━ v(t) Curve
DISPLACEMENT x(t) = t³ / 3 (CUBIC)
━ x(t) Curve
Leave a Reply