Question

Particles moves along the x-axis according to the equation x= 3t^2 - 2t + 3, where x is in meters and t is in seconds at t= 3s. Find a.) the position of the particle b.) it's velocity c.) it's acceleration​

Answer 1

EXPLANATION.

$\sf : \implies \: particle \: moves \: along \: the \: x - axis \: \\ \\ \sf : \implies \: equation \: = 3 {t}^{2} - 2t + 3$

$\sf : \implies \: 1) = the \: position \: of \: particle \: = x = 3 {t}^{2} - 2t + 3$

$\sf : \implies \: 2) = its \: velocity \\ \\ \sf : \implies \: velocity \: = v = \frac{dx}{dt} \\ \\ \sf : \implies \: \frac{dx}{dt} = 6t - 2 \: \: \: .....(1) \\ \\ \sf : \implies \: 6t - 2 = 0 \\ \\ \sf : \implies \: t = 3 \: seconds$

$\sf : \implies \: 3) = its \: acceleration \\ \\ \sf : \implies \: acceleration \: = a = \frac{dv}{dt} \\ \\ \sf : \implies \: \frac{dv}{dt} = 6t - 2 \\ \\ \sf : \implies \: \frac{dv}{dt} = 6(3) - 2 = 16 \: m {s}^{ - 2}$

Answer 2

Answer:

(a) 24m

(b)16 m/s

(c) 6 m/s²

Explanation:

x = 3t² - 2t + 3

(a) Position at t = 3s is

x = 3 × 3² - 2×3 + 3 = 27-6+3 = 24m

(b) velocity = dx/dt = d/dt (3t² - 2t + 3)

= 6t -2 = 6×3 - 2 = 18-2 = 16 m/s

(c) acceleration = dv/dt = d/dt (6t -2) = 6 m/s²