I need help with this problem?

Question

If a cheetah accelerates from rest at 7.8m/s squared in order to reach 70 mph in a distance of 30 meters. How much time has elapsed?

Answer 1

This is easy: d = v*t + a*t^2

But you had the cheetah at a standing start (v = 0 m/sec), so this simplifies to: d = a*t^2

Rearrange the equation to get : t^2 = d/a, so t = square root of (d/a)

d = 30 meters
a = 7.8 m/sec^2

t = (d/a)^½ = (30/7.8)^½ = 3.85^½ = 1.96 seconds

Answer 2

Another way:

70 mph = 70mph x 1609.3 meters/mile x 1hr/3600s = 31.3 m/s

So to get from rest to 31.3m/s at 7.8m/s^2 takes

31.3/7.8 = 4 seconds.


Note: the other answers did the math wrong by forgetting the
1/2!!!!

However, the numbers don't match here!! Either the 70mph
is wrong or the 30m.

Answer 3

d = v_i*t + 0.5*a*t^2
30 = 0 + 7.8*t^2
t^2 = 3.8
t = 1.96 sec