The velocity of a particle as a function of time is given by v(t) = (2.3 m/s) + (4.1 m/s²)t - (6.2 m/s³)t². What is the average acceleration of the particle between t = 1.0 s and t = 2.0 s? A) -13 m/s² B) -15 m/s² C) 13 m/s² D) 15 m/s² E) 0 m/s²

Question

Quizplus · Accepted Answer

Average acceleration between t=1.0s and t=2.0s is given by:

a_avg = (v(2) - v(1)) / (2 - 1)

where v(1) is the velocity at t=1.0s and v(2) is the velocity at t=2.0s.

v(1) = 2.3 + 4.1(1) - 6.2(1)^2 = 0.2 m/s

v(2) = 2.3 + 4.1(2) - 6.2(2)^2 = -25.4 m/s

Therefore,

a_avg = (-25.4 - 0.2) / (2 - 1) = -15.1 m/s^2 ≈ -15 m/s^2

So, the best choice is B.

The Velocity of a Particle as a Function of Time