To determine the distance the car moves in the 2.5 s starting from when the driver sees the deer, we can break it down into three parts:
1. The initial motion of the car before the brakes are applied.
2. The motion of the car when the brakes are applied.
3. The motion of the car after the brakes are released.
1. Initial Motion:
The car is moving at 95 km/h, which can be converted to m/s:
95 km/h × (1000 m/1 km) × (1 h/3600 s) = 26.39 m/s
To find the distance traveled during the initial motion, we use the formula:
distance = initial velocity × time
distance = 26.39 m/s × 0.50 s = 13.195 m
2. Motion with Brakes Applied:
The net force exerted by the brakes is 2400 N, which causes the car to decelerate.
Using Newton's second law of motion, F = ma, where F is the force, m is the mass, and a is the acceleration, we can calculate the acceleration of the car:
2400 N = (1200 kg) × a
a = 2400 N / 1200 kg
a = 2 m/s^2
To find the distance traveled during this time, we use the equation of motion:
distance = initial velocity × time + (1/2) × acceleration × time^2
distance = 26.39 m/s × 2.0 s + (1/2) × 2 m/s^2 × (2.0 s)^2
distance = 52.78 m + 2 m/s^2 × 4 s^2 / 2
distance = 52.78 m + 4 m
distance = 56.78 m
3. Motion after Brakes are Released:
After 2.0 s, the driver releases the brakes, and the car continues to move at a constant velocity.
The remaining time is 2.5 s - 0.50 s - 2.0 s = 0 s
Since the car moves at a constant velocity, the distance traveled during this time is:
distance = velocity × time
distance = 26.39 m/s × 0 s = 0 m
Therefore, the distance the car moves in the 2.5 s starting from when the driver sees the deer is:
13.195 m + 56.78 m + 0 m = 70.975 m (rounded to three decimal places).
A 1200kg car is moving at 95 km/ h when the driver notices a deer down the road. He immediately moves his foot toward the brake pedal, taking only 0.50 s before the car starts slowing down. The brakes cause a net force of 2400 N [backwards] on the car for 2.0 s. The deer then jumps out of the way and the driver lifts his foot off the brak e pedal. How far does the car move in the 2.5 s starting from when the driver sees the deer?
1 answer