A driver of a moving car at 20m/s finds a child on the road 50m ahead and stops the car 10m earlier to the child. If the mass of the car with driver is 1000kg, calculate the force exerted by the brakes of the car??
speed:
20-at=0
t = 20/a
distance:
20(20/a) - a/2 (20/a)^2 = 50-10
a = -5 m/s^2
F = ma = ...
5000kg
To calculate the force exerted by the brakes of the car, we can use Newton's second law, which states: Force = mass × acceleration.
First, let's find the initial velocity (u) of the car:
u = 20 m/s
Next, let's find the final velocity (v) of the car when it comes to a stop:
v = 0 m/s (since the car stops)
The distance (s) traveled by the car before coming to a stop is the difference between the distance to the child (50m) and the stopping distance (10m):
s = 50m - 10m = 40m
We can use the equation of motion to find the acceleration (a) of the car:
v^2 = u^2 + 2as
0^2 = 20^2 + 2a(40)
0 = 400 + 80a
-400 = 80a
a = -400/80
a = -5 m/s^2
Now, substitute the calculated acceleration and the mass of the car (1000kg) into Newton's second law to find the force exerted by the brakes:
Force = mass × acceleration
Force = 1000kg × (-5 m/s^2)
Force = -5000 N
The force exerted by the brakes of the car is -5000 Newtons. Note that the negative sign indicates that the force is in the opposite direction of the car's motion.
To calculate the force exerted by the brakes of the car, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a).
First, let's find the initial velocity (u) of the car before it stops. We know that the car is moving at a speed of 20 m/s, so u = 20 m/s.
Next, let's find the final velocity (v) of the car when it stops. The car comes to a stop, so v = 0 m/s.
Now, we can calculate the deceleration (a) of the car using the equation:
v^2 = u^2 + 2aS
Here, v = 0 m/s (final velocity), u = 20 m/s (initial velocity), and S = 10 m (distance traveled before stopping).
0^2 = 20^2 + 2a(10)
0 = 400 + 20a
-400 = 20a
a = -400/20
a = -20 m/s^2
Note that the acceleration is negative because it is in the opposite direction of motion (deceleration).
Given the mass (m) of the car with the driver is 1000 kg, we can now calculate the force (F) exerted by the brakes using the equation:
F = ma
F = (1000 kg) x (-20 m/s^2)
F = -20,000 N
The negative sign indicates that the force is in the opposite direction of motion.
Therefore, the force exerted by the brakes of the car is 20,000 Newtons (N) in the opposite direction of motion.