A particle travels as a function of time according to the formula s = 50 + 11t + 0.04t3 Where s is in meters and t is in seconds. Find the acceleration of the particle when t = 4.

Question

A particle travels as a function of time according to the formula

s = 50 + 11t + 0.04t³

Where s is in meters and t is in seconds. Find the acceleration of the particle when t = 4.

= ? m/sec²

 

Answer 1

Given: s = 50 + 11t + 0.04*t^3

s = meters, t = seconds

Find: Acceleration of particle when t = 4

Solution:

Acceleration is the second derivative.

s = 50 + 11t + 0.04*t^3

s' = 11 + (0.04)*(3)*t^2

s'' = (0.04)*(3)*(2)*t

s'' = (.24)*t

s'' = (.24)*(4) When t = 4

s'' = .96

When t = 4, acceleration is .96 m/s^2