If a body moves from rest in a straight line with nan acceleration (a) and another one with an acceleration (2a) covering the same distance ,the ratio between time of motion of the first body yo the second one is.....?

Question

if a body moves from rest in a straight line with nan acceleration (a) and another one with an acceleration (2a) covering the same distance ,the ratio between time of motion of the first body yo the second one is.....?

807 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-24T21:40:14

The ratio of times of first body vs second body was 1.414:1.

Using the kinematic formula #s = u*t + 1/2*a*t^2# with #u = 0#

First case:

#s = 1/2*a_1*(t_1)^2#

#t_1 = sqrt((2*s)/a_1) = 1.414*sqrt(s/a_1)#

Second case:

#s = 1/2*(2*a_1)*(t_2)^2#

#t_2 = sqrt(s/a_1)#

So the first body took 1.414 times longer.

I hope this helps,
Steve