SO a car has a mass of 1000 kg and is travelling at 20 m/s. the brakes exert a steady force of 5000 N. whats is the deceleration and how long does it take to stop the car
To find the deceleration of the car, we can use Newton's second law of motion: Force = mass × acceleration. Rearranging the formula, we get acceleration = Force / mass.
Given:
- Mass of the car (m) = 1000 kg
- Force exerted by the brakes (F) = 5000 N
Substituting these values into the formula, we can calculate the deceleration:
acceleration = Force / mass
acceleration = 5000 N / 1000 kg
acceleration = 5 m/s²
Therefore, the deceleration of the car is 5 m/s².
To find the time it takes to stop the car, we need to use the kinematic equation: velocity = initial velocity + (acceleration × time).
Given:
- Initial velocity (u) = 20 m/s
- Final velocity (v) = 0 m/s
- Acceleration (a) = -5 m/s² (negative sign indicates deceleration)
Substituting these values into the formula, we can find the time (t):
0 m/s = 20 m/s + (-5 m/s²) × t
Simplifying the equation:
0 m/s - 20 m/s = -5 m/s² × t
-20 m/s = -5 m/s² × t
Dividing both sides by -5 m/s²:
t = -20 m/s / -5 m/s²
t = 4 seconds
Therefore, it takes 4 seconds for the car to stop.
To find the deceleration of the car, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m * a). In this case, the force exerted by the brakes is 5000 N, and the mass of the car is 1000 kg.
So, we have:
Force (F) = 5000 N
Mass (m) = 1000 kg
Rearranging the equation to solve for acceleration (a):
a = F / m
a = 5000 N / 1000 kg
a = 5 m/s²
Therefore, the deceleration of the car is 5 m/s².
Now, to find the time it takes to stop the car, we can use the kinematic equation:
v = u + at
where:
v = final velocity (0 m/s, as the car is stopping)
u = initial velocity (20 m/s)
a = acceleration (-5 m/s², as it is decelerating)
t = time taken to stop
Rearranging the equation to solve for time (t):
t = (v - u) / a
t = (0 m/s - 20 m/s) / (-5 m/s²)
t = -20 m/s / -5 m/s²
t = 4 seconds
Therefore, it takes 4 seconds to stop the car.
a = f / m
divide the initial velocity by the acceleration to find the stopping time