Question

A woman drives 6 miles, accelerating uniformly from rest to 70 mph. How long does it take for her to reach 70 mph?

Answer 1

Ok so the acceleration, 70 mph, represents the slope, or first derivative, d '(t), of the distance funtion, d(t). The distance function is determined by taking the indefinite integral of the derivative.

Answer 2

d '(t)= 70

d(t) = ∫ [d '(t)] dt
d(t) = ∫ [70] dt
d(t) = 70t

d(t) = 6 mi.

6 = 70t
t = 6 / 70
t = 2/35 hr.
t = 12 min.

Answer 3

@madigrieve: if this is right.. than lets put in simple language..

Speed = distance/ time...

Answer 4

okay........ d= distance
t= time

Answer 5

well 70miles/hr= 32.08m/s and from here you'll get V=U+at substituting U=0 will give 32.08=a*t secondly, distance = 1/2 *a*t^2 from this you'll get a*t^2= 9.6 therefore just substitute value of t from first equation in to the second you'll get time=9.97 mins= 598.05 seconds