Question

solve at least one question (30 points)

Answer 1

Answer:

(a) the particle position = 135 m

(b) the velocity of the particle = 44 m/s

(c) the acceleration of the particle = 50 m/s²

Explanation:

Solution to Question 2.

Given;

velocity of a particle, v = 2 - 4t + 2t³

initial position at t = 0, s₀ = 3 m

(a) the particle position at t = 3 s

s = vt

s = (2 - 4t + 2t³)t

s = 2t - 4t² + 2t⁴

s = s₀ + s₃

s = s₀ + 2(3) - 4(3²) + 2(3⁴)

s = s₀ + 6 - 36 + 162

s = s₀ + 132 m

s = 3m + 132 m

s = 135 m

(b) the velocity of the particle at t = 3 s

v = 2 - 4t + 2t³ = 2 - 4(3) + 2(3)³

v = 44 m/s

(c) the acceleration of the particle at t = 3s

v = 2 - 4t + 2t³

$a = \frac{dv}{dt} \\\\a = \frac{d}{dt} (2 -4t + 2t^3)\\\\a = -4 + 6t^2$

a = -4 + 6(3)²

a = 50 m/s²