Charged Pion is an elementary particle with a mean lifetime

Charged Pion is an elementary particle with a mean lifetime of 2.6 x 10^(-8) seconds when measured in the rest frame of the Pion. If the Charged Pion travels at a speed of 0.98 c, how long will it travel during its lifetime? Note: Take the time dilation into account.

Solution

Here ,

mean lifetime , t0 = 2.6 *10^-8 s

speed of pion, v = 0.98 * c

Now , for the distance travelled

distance travelled = time * speed

distance travelled = t0/sqrt(1 - (v/c)^2) * v

distance travelled = 2.6 *10^-8/sqrt(1 - (0.98)^2) * 0.98 * 3 *10^8

distance travelled = 38.41 m

the distance travelled by pion is 38.41 m