Weird acceleration

Calculus Level 3

The velocity of a particle is given by $v(t) = \left \lfloor t - 5 \right \rfloor$ . Determine the total distance traveled by the particle on $0 \leqslant t \leqslant 8$ .

The answer is 18.

1 solution

Hobart Pao
May 16, 2016

To find total distance traveled on this interval, integrate the absolute value of velocity, or $\displaystyle \int_{0}^{8} \left| \left \lfloor t-5 \right \rfloor \right| \, dt$ . Before $t = 5$ , you have to be careful because you have to flip whatever is below the x axis above and make that positive due to absolute value. Overall, if you look at the floor function graph, you can see that this integral is equal to $5 + 4 + 3 + 2 + 1 + 0 + 1 + 2 = \boxed{18}$ .

It seems you typed $|\lfloor t+5 \rfloor |$ when you meant $|\lfloor t-5 \rfloor |$ . I have taken the liberty of editing this.

Alex G - 5 years, 1 month ago

Thanks for fixing it.

Hobart Pao - 5 years ago

Weird acceleration

The answer is 18.

1 solution

0 pending reports