A 2700 kg car traveling to the north is slowed down uniformly from an initial velocity of 29.8 m/s by a 7540 N braking force acting opposite the car’s motion.

a) What is the car’s velocity after 2.77 s? Answer in units of m/s.

F = M*a = -7540 N.

a = -7540/M = -7540/2700 = -2.79 m/s^2.

V = Vo + a*t, V = 29.8 - 2.79*2.77 = 22.1 m/s.

To find the car's velocity after 2.77 seconds, we can use the equation relating force, mass, and acceleration:

force = mass * acceleration

In this case, the force acting on the car is the braking force, and the acceleration is the rate at which the car slows down. Since the force is acting in the opposite direction of motion, the acceleration will be negative.

The acceleration can be calculated using Newton's second law:

acceleration = force / mass

Substituting the given values:

acceleration = 7540 N / 2700 kg

acceleration ≈ 2.79 m/s²

Now, we can use the equation of motion:

velocity = initial velocity + (acceleration * time)

Substituting the given values:

velocity = 29.8 m/s + (-2.79 m/s² * 2.77 s)

velocity ≈ 29.8 m/s - 7.75 m/s

velocity ≈ 22.05 m/s

Therefore, the car's velocity after 2.77 seconds is approximately 22.05 m/s.

To find the car's final velocity after 2.77 seconds, we can use the equation of motion:

v = u + at

where:
v = final velocity
u = initial velocity
a = acceleration
t = time

Here, the car is being slowed down, so the acceleration will be in the opposite direction to the initial velocity. Since the acceleration is uniform, we can use the following equation to calculate it:

F = ma

where:
F = force
m = mass
a = acceleration

Rearranging this equation, we can solve for acceleration:

a = F / m

Plugging in the given values:
F = 7540 N (braking force)
m = 2700 kg (mass of the car)

We get:

a = 7540 N / 2700 kg
a ≈ 2.796 m/s² (rounded to three decimal places)

Now, we can substitute the values of u, a, and t into the first equation:

v = 29.8 m/s + (2.796 m/s²) * 2.77 s

Calculating this expression, we find:

v ≈ 29.8 m/s + 7.749 m/s
v ≈ 37.549 m/s (rounded to three decimal places)

Therefore, the car's velocity after 2.77 seconds is approximately 37.549 m/s.