# Answer to Question #723 in Mechanics | Relativity for Rooky

Question #723

In an automobile race, the cars are started with a starter car traveling at 31.5 m/sec. If the lead car has an average acceleration of 4.3 m/sec^2 during the first 3 seconds, how fast was it traveling at the end of 3 seconds and how far did it go?

Expert's answer

We have for the leading car:

v-v_0=a*t =>v= a*t+v_0 = 4.3*3 + 31.5 = 44.4 m/s

for the distance we have either

x=1/2*a*t^2 + v_0*t =1/2*4.3*3^2 + 31.5*3= 113.85 m

or

v^2-(v_0)^2=2*a*x => x=[v^2-(v_0)^2]/(2*a) = [44.4^2- 31.5^2]/(2*4.3) = 113.85 m

v-v_0=a*t =>v= a*t+v_0 = 4.3*3 + 31.5 = 44.4 m/s

for the distance we have either

x=1/2*a*t^2 + v_0*t =1/2*4.3*3^2 + 31.5*3= 113.85 m

or

v^2-(v_0)^2=2*a*x => x=[v^2-(v_0)^2]/(2*a) = [44.4^2- 31.5^2]/(2*4.3) = 113.85 m

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