I can't get word problems

Question

A driver going down a straight highway is traveling at 70ft/sec on cruise control when he begins accelerating at a rate of 4.2 ft/sec² . The final velocity of the car is given by the function V(t) = 21/5t + 70, where V(t) is the velocity at time t.

If the car is traveling at 100 ft/sec, for how long did it accelerate? (Round to the nearest tenth of a second.)

Answer 1

V(t) = (21/5)t + 70

100 = (21/5)t + 70

30 = (21/5)t

30·5/21 = t

150/21 = 50/7 ≈ 7.14 sec = t

Answer 2

Note that v(0) = 70 ft/sec.  Acceleration takes place from time t = 0 up to an unknown t, which you must solve for.  Set v(t) = 100 ft/s and solve for t.

 

100 = 4.2t + 70

 

(4.2 = 21/5)

 

t = (100 - 70)/4.2 ≅ 7.1 sec