The Skill Builder question asks for the acceleration of a particle at t = 5 s, given x = 3t - 2t³ and y = 15t.
Step-by-step solution:
X-direction:
- vₓ = dx/dt = 3 - 6t²
- aₓ = dvₓ/dt = -12t
At t = 5 s: aₓ = -12 × 5 = -60 m/s²
Y-direction:
- vᵧ = dy/dt = 15 m/s (constant)
- aᵧ = dvᵧ/dt = 0
Net acceleration:
a_net = aₓ î + aᵧ ĵ = -60î m/s²
The correct answer is (c) -60î m/s²
Wait - let me recheck the options. The image shows:
- (a) -70î m/s
- (b) -60î m/s
- (c) -80î m/s²
- (d) -35î m/s
The only option with correct units (m/s²) for acceleration is (c), but the calculation gives -60î m/s². The answer matching the calculation is (b) -60î m/s² - however the units on (b) say m/s which is a typo in the textbook. The correct answer is (b) -60î m/s² (acceleration, not velocity).
Answer: (b) -60î m/s²
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