An ice sled powered by a rocket engine starts
from rest on a large frozen lake and accelerates
at 15.0 m/s
2
. At t1 the rocket engine is
shut down and the sled moves with constant
velocity v for another t2 s. The total distance
traveled by the sled is 5.60 × 10
3 m and the
total time is 96.7 s.
Find t1.
To find t1, we can use the equations of motion for the sled. Let's break down the problem into two parts:
Part 1: Acceleration
The sled starts from rest and accelerates at 15.0 m/s^2 for a time t1. Using the equation of motion for constant acceleration:
Distance traveled during acceleration = (0.5) * acceleration * (time)^2
We don't know the exact distance traveled during the acceleration phase, so let's call it d1.
d1 = (0.5) * 15.0 * (t1)^2
Part 2: Constant velocity
After the rocket engine is shut down, the sled moves with constant velocity v for another time t2. During this phase, the sled covers a distance of v * t2.
d2 = v * t2
Given that the total distance traveled by the sled is 5.60 × 10^3 m, we can write an equation for the total distance:
Total distance = d1 + d2
5.60 × 10^3 = (0.5) * 15.0 * (t1)^2 + v * t2
We're also given that the total time is 96.7 s, so we can write an equation for the total time:
Total time = t1 + t2
96.7 = t1 + t2
Now we have two equations with two unknowns (t1 and t2). We can solve these equations simultaneously to find t1.