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) = 85t 8t + 14 (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

Answer:

(a) $0.408m/sec^2$

(b) $0.134m/sec^2$

(c) $0.039m/sec^2$

Step-by-step explanation:

We have given velocity as function of t $v(t)=\frac{85t}{(8t+14)}$

Acceleration is equation rate if change of velocity with respect to time

So $a=\frac{dv}{dt}=\frac{(8t+14)85-85t\times 8}{(8t+14)^2}$

(a) Acceleration at t = 5 sec

$a=\frac{(8\times 5+14)85-85\times 5\times 8}{(8\times 5+14)^2}=0.408m/sec^2$

(b) Acceleration at t = 10 sec

$a=\frac{(8\times 10+14)85-85\times 10\times 8}{(8\times 10+14)^2}=0.134m/sec^2$

(c) Acceleration at t = 20 sec

$a=\frac{(8\times 20+14)85-85\times 20\times 8}{(8\times 20+14)^2}=0.039m/sec^2$