A car which has a mass of 1.36 tonnes is travelling at 26.8m/s on a level road when the driver brings the car to an emergency stop using only the brakes. A time interval of 4.18s is required to bring the car to a stop.
1. Calculate the position of the car while the car is coming to a stop. Assume x ₀= 0
2. Calculate the braking force acting on the car while the car comes to a stop.
To answer these questions, we need to use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. The equation is:
F = m * a
1. Calculate the position of the car while it is coming to a stop:
To find the position of the car, we need to first calculate its acceleration. We can use the equation:
a = (v - u) / t
where:
a = acceleration
v = final velocity (0 m/s because the car comes to a stop)
u = initial velocity (26.8 m/s)
t = time interval (4.18 s)
Substituting the values into the equation, we find:
a = (0 - 26.8) / 4.18
a ≈ -6.37 m/s²
Now, we can calculate the position (displacement) of the car using the equation:
s = ut + (1/2) * a * t²
where:
s = displacement
u = initial velocity
t = time interval
a = acceleration
Substituting the values into the equation, we find:
s = 26.8 * 4.18 + (1/2) * (-6.37) * (4.18)²
s ≈ 56.12 meters
Therefore, the position of the car while it is coming to a stop is approximately 56.12 meters.
2. Calculate the braking force acting on the car while it comes to a stop:
To find the braking force, we need to use the equation:
F = m * a
where:
F = force
m = mass (1.36 metric tons = 1360 kg)
a = acceleration (-6.37 m/s²)
Substituting the values into the equation, we find:
F = 1360 * (-6.37)
F ≈ -8679.2 Newtons
The negative sign indicates that the force is in the opposite direction of the car's motion. Therefore, the magnitude of the braking force acting on the car while it comes to a stop is approximately 8679.2 Newtons.
mass = 1360 kg = m
Vi = 26.8
v = Vi + a t
0 = 26.8 + 4.18 t
so
a = -26.8/41.8
use that a
x = 0 + 26.8 t -(1/2)(26.8/41.8) t^2
ah come on F = m a