Question

A car is moving at 20.0 m/s [N] when it begins to constantly accelerate to a final velocity of 10.0 m/s [E]. The magnitude of its displacement during this time is 1.50 x 10^2 m.

How long did the acceleration last?

I know that the answer is 13.4 s, but can you show me how you got there?

This is what I have:

Table: horiz || vert
displacment: d(x) 7.0 m d(y) 3.05 - 2.25
acceleration: not given
velocity initial: vix(9 cos 0)

Answer 1

X = 10 m/s
Y = 20 m/s

V^2 = X^2 + Y^2
V^2 = 10^2 + 20^2 = 500
V = 22.4 m/s = Resultant velocity.

a = (V-Vo)/t = (22.4-0)/t = 22.4/t m/s^2

d = 0.5*a*t^2 = 150
0.5*(22.4/t)*t^2 = 150 m
(11.2/t)*t^2 = 150
11.2t = 150
t = 13.4 s.