Expert: Ahmed Salami - 8/26/2009

Question
the runner continue to run 6m/s until the end of the race. after crossing the finish line the runner decelerates at 2 m/s2, how long will it take him to stop? Haow far does the runner travel while running?

Answer
Hi Angel,
Here, we use the equation of motion
v = u + at
where v is the final velocity
u is the initial velocity
a is the acceleration
and t is the time taken
The runner has an initial velocity of 6m/s but eventually comes to a stop i.e a final velocity of 0m/s. Since he is slowing down the value of acceleration is negative i.e -2m/s². And so,
0 = 6 + (-2)t
0 = 6 - 2t
2t = 6
t = 3s
To find the distance covered during that time, we use the equation
v² = u² + 2as
where s is the distance covered
0² = 6² + 2(-2)s
0 = 36 - 4s
4s = 36
s = 9m

Regards