How large an average force is required to stop a 1400-kg car in 5.0 s if the car’s initial speed is 25 m/s?
force = change in momentum/time = m a if m constant
Force * time = change in momentum
F * 5 = 1400 * 25
F = 1400 * 5 = 7000 Newtons
To answer this question, we can use Newton's second law of motion. According to this law, the force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's calculate the acceleration of the car using the given information.
We know that the initial speed of the car is 25 m/s, and the time it takes to stop is 5.0 s. The final speed of the car when it stops will be 0 m/s, as it comes to a complete halt.
The acceleration of the car can be calculated using the equation:
acceleration (a) = (final velocity - initial velocity) / time
Substituting the values into the equation:
a = (0 m/s - 25 m/s) / 5.0 s
a = -25 m/s / 5.0 s
a = -5 m/s²
The negative sign indicates that the car is decelerating, or slowing down.
Now, let's calculate the force required to decelerate the car.
force (F) = mass (m) * acceleration (a)
Given that the mass of the car is 1400 kg, and the acceleration is -5 m/s²:
F = 1400 kg * (-5 m/s²)
F = -7000 kg·m/s²
The force required to stop the car is -7000 kg·m/s². The negative sign indicates that the force is in the opposite direction of the initial motion of the car.