Answer:
The traveled distance is 63.0 m
Explanation:
We can write the equation for the acceleration as the variation of the velocity over time:
dv/dt = a
where
dv/dt = variation of velocity over time
a = constant acceleration
Then separating variables, we can solve the equation:
dv = a dt
Integrating between the initial velocity ( v0) and final velocity (v) and between t = 0 and t = t.
v - v0 = a · t
v = v0 + a · t
This is the equation of velocity at time t.
Now, we can write the velocity as the variation of the position over time (dx/dt). Then:
dx/dt = v0 + a · t
Separating varibles:
dx = v0 · dt + a · t · dt
Integrating between the initial position (x0) and final position (x) and between t = 0 and t
x -x0 = v0 · t + 1/2 · a · t²
x = x0 + v0 · t + 1/2 · a · t²
This is the equation of position at time t.
Now, we know that the velocity at time 6.00 s is 0. Then:
v = v0 + a · t
Solving for a
(v -v0)/t = a
(0- 21.0 m/s)/6.00s = -3.50 m/s² = a
Then, using this acceleration in the equation of the position:
x = x0 + v0 · t + 1/2 · a · t²
x = 0 m + 21.0 m/s · 6.00 s + 1/2 · (-3.50 m/s²) · (6.00 s)²
x = 63.0 m
The traveled distance is 63.0 m
