Calculate initial speed and acceleration given position (on x-axis) and time

[towng34]

Homework Statement

Help! I have no idea where to begin for this!

You are driving along a straight section of roadway (x-axis). You spot a police officer and apply the brakes, slowing down at a constant rate. Your positions (in meters) at successive time intervals of 0.465 s are tabulated below as function of time. (1) Calculate the initial speed (i.e., the speed at t=0, the time at which the brakes are first applied.). (2) Calculate your acceleration along the x-axis, ax.
x (m) 5.00 21.94 38.25 53.93
t (s) 0.000 0.465 0.930 1.395

Homework Equations

x = x0 + v0t + (1/2)at^2
v = v0 + at
v^2 = v0^2 + 2a(x-x0)

The Attempt at a Solution

 

[rl.bhat]

Hi towng34, welcome to PF.

If t is the successive interval of time, then

x1 = xo + vo(t) +1/2*a*t^2...(1)

x2 = xo + vo*(2t) +1/2* a*(2t)^2 ...(2)

Find x2 - 2*x1 and solve for a. From that you can find vo.