Answer:
129 m because the average velocity is 13.9 m/s, the change in velocity
divided by the acceleration is the time, and the time multiplied by the
average velocity is the distance. ⇒ answer C
Explanation:
Lets explain how to solve the problem
The given is:
The care is able to stop with an acceleration of -3 m/s²
→ The final velocity = 0 and acceleration = -3 m/s²
Calculate the distance required to stop from a velocity of 100 km/h
→ Initial velocity = 100 km/h
At first we must to change the unite of the initial velocity from km/h
to m/s because the units of the acceleration is m/s²
→ 1 km = 1000 meters and 1 hr = 3600 seconds
→ 100 km/h = (100 × 1000) ÷ 3600 = 27.78 m/s
The initial velocity is 27.78 m/s
Acceleration is the rate of change of velocity during the time,
then the time is the change of velocity divided by the acceleration
→ [tex]t=\frac{v-u}{a}[/tex]
where v is the final velocity, u is the initial velocity, t is the time and
a is the acceleration
→ v = 0 , u = 27.78 m/s , a = -3 m/s²
Substitute these values in the rule
→ [tex]t=\frac{0-27.78}{-3}=9.26[/tex] seconds
The time to required stop is 9.26 seconds
We can calculate the distance by using the rule:
→ s = ut + [tex]\frac{1}{2}[/tex] at²
→ u = 27.78 m/s , t = 9.26 s , a = -3 m/s²
Substitute these values in the rule
→ s = 27.78(9.26) + [tex]\frac{1}{2}[/tex] (-3)(9.26) = 128.6 ≅ 129 m
The distance required to stop is 129 m
Average velocity is total distance divided by total time
→ Total distance = 129 m and total time = 9.26 s
→ average velocity = 129 ÷ 9.26 = 13.9 m/s
The average velocity is 13.9 m/s
So the time multiplied by the average velocity is the distance
The answer is C
129 m because the average velocity is 13.9 m/s, the change in
velocity divided by the acceleration is the time, and the time
by the average velocity is the distance.
