Speed-time graphs

Hi Rauhan

Given that the total distance travelled is 1.4 km, and the acceleration is 4m/s^2 for the the first T second, find:

(a) the value of V

(b) the value of T

I will assume that the object is originally at rest at the origin. From time 0 the acceleration is a constant 4m/s^2  

And that after T seconds it has traveled 1.4 km.

There are a lot of assumptions here

$\ddot x=4\\ \dot x=4t+k \qquad but\;\;k=0\\ \dot x=4t\\~\\ x=(4/2)t^2+c \qquad c=0\\ x=2t^2\\ \text{When t=T, x=1.4}\\ 1.4=2T^2\\ T^2=1.4/2 = 0.7\\ T=\sqrt{7}\approx 2.646\;seconds$