Question

After a big snowfall, you take your favorite rocket‑powered sled out to a wide field. The field is 223 m223 m across, and you know that your sled accelerates at a rate of 3.25 m/s23.25 m/s2 when the rocket is on. How much time will it take the sled to cross the field starting from rest, assuming the rocket is on the whole time?

Answer 1

Answer:

11.7 s

Explanation:

In this problem, the rocket is moving in a uniform accelerated motion. We have the following data:

d = 223 m, the distance that the sled has to cover

$a=3.25 m/s^2$, the acceleration of the rocket

We can use therefore the following SUVAT equation:

$d=ut+\frac{1}{2}at^2$

where

d is the distance

u = 0 is the initial velocity of the sled (it starts from rest)

t is the time

a is the acceleration

Re-arranging the equation and substituting the numbers, we find the time it takes for the rocket to cross the field:

$d=\frac{1}{2}at^2\\t=\sqrt{\frac{2d}{a}}=\sqrt{\frac{2(223)}{3.25}}=11.7 s$