A particle moves with a velocity function v=20-10t. Calculate the maximum distance travelled by the particle before stopping

Answer 1

Given that you want to determine the distance traveled until the particle stops, you need to determine how much time goes by. When the particle stops the velocity is zero. Since v(t) = 20 - 10t, to find the time, set the velocity equal to zero and solve for t:

0 = 20 - 10t

t = 2

Now, to find the displacement between t = 0 and t = 2, take the integral of the velocity:

₀∫²20 - 10t dt = 20t - 5t² evaluated between 0 and 2 = [20(2) - 5(2²)] - [20(0) - 5(0²)] = 20 - 0 = 20 so the particle travels 20 "units" before stopping.

Note that the displacement you calculate in this fashion is NOT always the same as the distance traveled. You would need to determine if there are any reversals in direction that need to be accounted for (traveling forward 60 meters then backwards 40 meters results in a displacement of 20 meters but a total distance traveled of 100 meters). But in this case, the velocity goes from 10 at t = 0 to zero at t = 2 so there are no changes of direction to account for.