The velocity of an automobile starting from rest is given by the equation below, where v is measured in feet per second and t is the time in seconds.

Question

The velocity of an automobile starting from rest is given by the equation below, where v is measured in feet per second and t is the time in seconds. (Round your answers to three decimal places.)

v(t) = 120t

7t + 16

 

(a) Find the acceleration at 5 seconds.

 ft/sec²

(b) Find the acceleration at 10 seconds.

 ft/sec²

(c) Find the acceleration at 20 seconds.

 ft/sec²

Answer 1

a(t) = v'(t) = 120(7t + 16 - 7t)/(7t + 16)² = 1920/(7t + 16)².;

a(5) = 1920/41² = 1.142 ft/s²

a(10) = 1920/86² = 0.260 ft/s²;

a(20) = 1920/156² = 0.0789 ft/s².