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shubham raj · Jul 20, 2011, 08:20 AM

The reaction time for an automobile driver is 0.7 seconds. If the automobile can be deaccelerated at 5 metre per second square, calculate the total distance travelled in coming to stop from an initial velocity of 8.33 metre per second after a signal is observed.

ebaines · Jul 20, 2011, 11:09 AM

Think of this in two parts:

1) During the initial 0.7 seconds reaction time how far does the car travel? It's initial velocity is 8.33 m/s:

$<br /> d_1 = v_i t<br />$

2) As the car deccelerates, how far does it go? Use:

$<br /> v_f^2 - v_i^2 = 2 a d_2<br />$

Here you know $v_f = 0$ , $v_i = 8.33 m/s$ , and $a = -5m/s^2$ . Solve for $d_2$ .

Then add $d_1$ and $d_2$ together to get the total distance.