A car has constant declaration of 10 km/h/s until it stops. If the car's initial velocity is 120 km/h, determine its stopping distance.
To determine the stopping distance of the car, we need to first find the time it takes for the car to come to a stop. We can use the formula:
v = u + at
where:
v = final velocity (0 km/h, since the car comes to a stop)
u = initial velocity (120 km/h)
a = acceleration (-10 km/h/s)
t = time
Rearranging the formula to solve for time:
t = (v - u) / a
Substituting the given values into the formula:
t = (0 - 120) / (-10)
t = 12 seconds
Next, we can find the stopping distance using the formula:
s = ut + (1/2)at^2
where:
s = stopping distance
u = initial velocity (120 km/h)
t = time (12 seconds)
a = acceleration (-10 km/h/s)
Substituting the given values into the formula:
s = (120 * 12) + (1/2) * (-10) * (12^2)
s = 1440 + 1/2 * (-10) * 144
s = 1440 - 720
s = 720 km
Therefore, the stopping distance of the car is 720 km.
To determine the stopping distance of the car, we need to calculate the time it takes for the car to stop and then multiply it by the average velocity during that time.
First, let's calculate the time it takes for the car to stop. We can use the formula:
time = (final velocity - initial velocity) / acceleration
The initial velocity is given as 120 km/h, and the final velocity is 0 km/h since the car stops. The acceleration is given as a constant -10 km/h/s (notice the negative sign indicates deceleration).
Converting the velocity values to m/s for unit consistency:
initial velocity = 120 km/h * (1000 m/1 km) * (1 h/3600 s) = 33.33 m/s
final velocity = 0 km/h * (1000 m/1 km) * (1 h/3600 s) = 0 m/s
Now we can calculate the time:
time = (0 m/s - 33.33 m/s) / (-10 km/h/s * (1000 m/1 km) * (1 h/3600 s))
time = -33.33 m/s / (-10 m/s²)
time = 3.333 s
Now that we know it takes 3.333 seconds for the car to stop, we can calculate the stopping distance. The average velocity during this time can be calculated by averaging the initial and final velocity:
average velocity = (initial velocity + final velocity) / 2
average velocity = (33.33 m/s + 0 m/s) / 2
average velocity = 16.67 m/s
Finally, we can calculate the stopping distance using the formula:
stopping distance = average velocity * time
stopping distance = 16.67 m/s * 3.333 s
stopping distance = 55.56 meters
Therefore, the stopping distance of the car is 55.56 meters.
v²-u²=2aS
S=distance travelled (=stopping distance)
a=acceleration
= 10 km h-1 s-1
= ? m s-2
u=initial velocity = 120 km h-1
= ? m s-1
v=final velocity = 0 m s-1
Convert all quantities to metres and seconds.
Solve for S.