To stop a car, first you require a certain reaction time to begin braking; then

Question

To stop a car, first you require a certain reaction time to begin braking; then
the car slows under the constant braking. Suppose that the total distance moved by your car during these two phases is 56.7 m when its initial speed is 80.5 km/h, and 24.4 m when its initial speed is 48.3 km/h. What are (a) your reaction time and (b) the magnitude of the braking acceleration?

Explanation / Answer

Which step is not clear??? may be you mean the calculation of equation 1 & 2??? I will calculate it in more detail, to clarify the solution for you: Starting from the two equations: (80.5)^2-2*a*(56.7-t*80.5)=0......(equation 1) (48.3)^2-2*a*(24.4-t*48.3)=0.......(equation 2) (80.5)^2=2*a*(56.7-t*80.5)..... from equation (1) then 80.5=2*a*(56.7-t) -----> then we get a=80.5/[2*(56.7-t)] By substituting the value of (a) that we get it from equation (1) into equation (2), we have: (48.3)^2-2*[80.5/2*(56.7-t)]*(24.4-t*48.3)=0 48.3=2*[80.5/2*(56.7-t)]*(24.4-t) (48.3*56.7)-48.3t=80.5*24.4-80.5t------> t=24.05 as we get a=80.5/[2*(56.7-t) , and t=24.05 then a=1.233 Good Luck!

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