When a driver presses the brake pedal, his car stops with an acceleration of -8.7 m/s2. How far will the car travel while coming to a complete stop if its initial speed was 10 m/s?
bals juice
To find the distance traveled by the car while coming to a complete stop, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, as the car comes to a complete stop)
u = initial velocity (10 m/s)
a = acceleration (-8.7 m/s^2)
s = distance traveled
Rearranging the equation to solve for s:
s = (v^2 - u^2) / (2a)
Plugging in the given values:
s = (0^2 - 10^2) / (2 * -8.7)
s = (-100) / (-17.4)
s = 5.75 meters
Therefore, the car will travel a distance of 5.75 meters while coming to a complete stop.
To find the distance the car will travel while coming to a complete stop, we can use the equations of motion. In this case, we'll use the equation:
v^2 = u^2 + 2as
where:
- v is the final velocity (which is 0 m/s since the car is coming to a complete stop)
- u is the initial velocity (10 m/s)
- a is the acceleration (-8.7 m/s^2)
- s is the distance traveled while decelerating
Substituting the known values into the equation:
0^2 = (10 m/s)^2 + 2(-8.7 m/s^2)(s)
Simplifying:
0 = 100 m^2/s^2 - 17.4 m/s^2(s)
Rearranging the equation to solve for s:
17.4 m/s^2(s) = 100 m^2/s^2
s = 100 m^2/s^2 / 17.4 m/s^2
s = 5.75 m
Therefore, the car will travel approximately 5.75 meters while coming to a complete stop.
It takes the car 10/8.7 = 1.149 seconds to stop
s = 10t - 4.35t^2
so plug in t = 1.149 to find the distance