Rectilinear Motion Problems And Solutions Mathalino Upd High Quality ❲UPDATED 2024❳

v(4) = 4(4) - (64)/3 + 3 = 16 - 21.333 + 3 = -2.333 m/s (moving negative direction).

✅ Answer: (a) v(t)=4t - t³/3+3; (b) s(t)=2t² - t⁴/12+3t+2; (c) -2.333 m/s; (d) 22.667 m. Problem 4: Car A and Car B are on the same straight road. Car A is 100 m ahead of Car B at t=0. Car A moves with constant velocity 20 m/s. Car B starts from rest at t=0 and accelerates at 2 m/s². How long will it take for Car B to overtake Car A? Solution (Mathalino approach – use relative motion or equal position): Let s=0 at Car B’s initial position. For Car A: s_A = 100 + 20t (since 100 m ahead at t=0, vel=20) For Car B: s_B = 0 + 0·t + ½ (2) t² = t² rectilinear motion problems and solutions mathalino upd

6t² – 18t + 12 = 0 → divide 6: t² – 3t + 2 = 0 → (t-1)(t-2) = 0 Thus at t = 1 s and t = 2 s , the particle is momentarily at rest. v(4) = 4(4) - (64)/3 + 3 = 16 - 21

v = ds/dt = 4t - t³/3 + 3 → ds = (4t - t³/3 + 3) dt s(t) = ∫(4t - t³/3 + 3) dt = 2t² - t⁴/12 + 3t + D At t=0, s=2 → 2 = 0 - 0 + 0 + D → D=2. Thus s(t) = 2t² - t⁴/12 + 3t + 2 m. Car A is 100 m ahead of Car B at t=0

✅ Answer: The second stone’s initial velocity is . 4. Problem Set #3: Motion with Variable Acceleration (Integration) Problem 3: The acceleration of a particle moving along a straight line is given by a = 4 - t² (in m/s²). At t=0, v=3 m/s and s=2 m. Find (a) v as a function of t, (b) s as a function of t, (c) the velocity when t=4 s, and (d) the displacement from t=0 to t=4 s. Solution: a) Velocity: a = dv/dt = 4 - t² → dv = (4 - t²) dt Integrate: v(t) = ∫(4 - t²) dt = 4t - t³/3 + C At t=0, v=3 → 3 = 0 - 0 + C → C=3. Thus v(t) = 4t - t³/3 + 3 m/s.

Stone 2 is thrown 1 second later, so its travel time = t - 1 = 2.193 s. Initial velocity u (downward positive): y = u·t₂ + ½ g t₂² → 50 = u(2.193) + ½ (9.81)(2.193)² ½(9.81)(4.809) = 23.58 Thus 50 = 2.193u + 23.58 → 2.193u = 26.42 → u ≈ 12.04 m/s downward.

s(4) = 2(16) - (256)/12 + 3(4) + 2 = 32 - 21.333 + 12 + 2 = 24.667 m s(0)=2 m → Displacement = 24.667 - 2 = 22.667 m .