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