A car with an initial speed of 21.9 km/h accelerates at a uniform rate of 0.89 m/s
2
for 3.7
s.
Find the final speed of the car.
Find the displacement of the car after that time.
Answer in units of km
Vf = Vi + a t
Vf = 21.9*10^3/3600 + .89(3.7)
in meters/ second
right then it is at
x = 0 + 21.9*10^3/3600 * 3.7 + (1/2)(.89)(3.7)^2
in meters
divide by 1000 for km
after that it continues at Vf forever and travels an additional distance d
d = Vf t
remember to divide by 1000 to get km again
To find the final speed of the car, we can use the equation:
final speed = initial speed + (acceleration * time)
Given:
Initial speed = 21.9 km/h
Acceleration = 0.89 m/s^2
Time = 3.7 s
First, let's convert the initial speed from km/h to m/s:
Speed (m/s) = Speed (km/h) * (1000 m / 1 km) * (1 h / 3600 s)
So, the initial speed in m/s is:
21.9 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 6.0833333 m/s (approximately 6.08 m/s)
Now, let's calculate the final speed:
final speed = 6.08 m/s + (0.89 m/s^2 * 3.7 s)
final speed = 6.08 m/s + 3.293 m/s
final speed = 9.373 m/s (approximately 9.37 m/s)
To find the displacement of the car, we can use the equation:
displacement = (initial speed * time) + (0.5 * acceleration * time^2)
Given:
Initial speed = 6.08 m/s
Acceleration = 0.89 m/s^2
Time = 3.7 s
Let's calculate the displacement:
displacement = (6.08 m/s * 3.7 s) + (0.5 * 0.89 m/s^2 * (3.7 s)^2)
displacement = 22.456 m + (0.5 * 0.89 m/s^2 * 13.69 s^2)
displacement = 22.456 m + 6.0856 m
displacement = 28.5416 m (approximately 28.54 m)
Finally, to convert the displacement from meters to kilometers, we can divide it by 1000:
displacement = 28.54 m / 1000 = 0.02854 km
Therefore, the final speed of the car is 9.37 m/s and the displacement after 3.7 seconds is approximately 0.02854 km.