Answer:
38.7 units
Explanation:
a = 3.00 t² – 4.20 t
Integrate to find velocity as a function of time.
v = ∫ a dt
v = ∫ (3.00 t² – 4.20 t) dt
v = 1.00 t³ – 2.10 t² + C
The object starts at rest, so at t = 0, v = 0.
0 = 1.00 (0)³ – 2.10 (0)² + C
0 = C
v = 1.00 t³ – 2.10 t²
Integrate to get position as a function of time.
x = ∫ v dt
x = ∫ (1.00 t³ – 2.10 t²) dt
x = 0.250 t⁴ – 0.700 t³ + C
Find the difference in positions between t = 4.50 and t = 0.
Δx = [0.250 (4.50)⁴ – 0.700 (4.50)³ + C] – [0.250 (0)⁴ – 0.700 (0)³ + C]
Δx = 0.250 (4.50)⁴ – 0.700 (4.50)³
Δx = 38.7
The object moves 38.7 units.
