a. For 6.00 seconds:
s
=
(
12.0
m/s
)
×
(
6.00
s
)
+
1
2
×
(
−
1.60
m/s
2
)
×
(
6.00
s
)
2
s=(12.0m/s)×(6.00s)+
2
1
×(−1.60m/s
2
)×(6.00s)
2
b. For 9.00 seconds:
s
=
(
12.0
m/s
)
×
(
9.00
s
)
+
1
2
×
(
−
1.60
m/s
2
)
×
(
9.00
s
)
2
s=(12.0m/s)×(9.00s)+
2
1
×(−1.60m/s
2
)×(9.00s)
2
To calculate the value of s for 6.00 seconds, we plug in the given values into the equation:
s = (12.0 m/s) × (6.00 s) + (1/2) × (-1.60 m/s^2) × (6.00 s)^2
s = 72.0 m + (-1.60 m/s^2) × 36.0 s^2
s = 72.0 m - 57.6 m
s = 14.4 m
Therefore, for 6.00 seconds, s = 14.4 m.
To calculate the value of s for 9.00 seconds, we plug in the given values into the equation:
s = (12.0 m/s) × (9.00 s) + (1/2) × (-1.60 m/s^2) × (9.00 s)^2
s = 108.0 m + (-1.60 m/s^2) × 81.0 s^2
s = 108.0 m - 129.6 m
s = -21.6 m
Therefore, for 9.00 seconds, s = -21.6 m.
a. To find the distance traveled for 6.00 seconds, we can use the equation s = (v0 * t) + (1/2 * a * t^2), where s is the distance, v0 is the initial velocity, t is the time, and a is the acceleration. Plugging in the given values:
s = (12.0 m/s) * (6.00 s) + (1/2) * (-1.60 m/s^2) * (6.00 s)^2
s = 72.0 m - 28.8 m
s = 43.2 m
So, the distance traveled for 6.00 seconds is 43.2 meters.
b. To find the distance traveled for 9.00 seconds, we can use the same formula:
s = (12.0 m/s) * (9.00 s) + (1/2) * (-1.60 m/s^2) * (9.00 s)^2
s = 108.0 m - 64.8 m
s = 43.2 m
So, the distance traveled for 9.00 seconds is also 43.2 meters.