A car enters the freeway with a speed of 6.9
m/s and accelerates uniformly for 3.3 km in
2.8 min.
How fast is the car moving after this time?
Answer in units of m/s
t = 2.8min * 60s/min = 168 s.
d = Vo*t + 0.5a*t^2 = 3300 m.,
6.9*168 + 0.5a*(168)^2 = 3300
1159 + 14112a = 3300
14112a = 3300-1159 = 2141
a = 0.152 m/s^2.
V = Vo + at = 6.9 + 0.152*168=25.5 m/s.
oops! It is Henry Not anonymous.
First, we need to convert the distance and time to consistent units.
1. Convert the distance from kilometers to meters:
- 3.3 km * 1000 m/km = 3300 m
2. Convert the time from minutes to seconds:
- 2.8 min * 60 s/min = 168 s
Now, let's calculate the acceleration:
3. Use the formula for uniform acceleration:
- a = (v - u) / t
where:
a = acceleration
v = final velocity (unknown)
u = initial velocity = 6.9 m/s
t = time = 168 s
4. Rearrange the formula to solve for v (final velocity):
- v = a * t + u
5. Calculate the acceleration:
- a = (3300 m - 0 m) / 168 s
- a = 19.643 m/s² (rounded to four decimal places)
6. Substitute the values into the formula:
- v = (19.643 m/s²) * (168 s) + 6.9 m/s
7. Simplify the equation:
- v = 3300.024 m/s
Therefore, the car is moving at approximately 3300 m/s after 2.8 minutes.
To determine the final speed of the car, we will first convert the given distance and time into the appropriate units, and then use the equation of motion to calculate the final speed.
1. Convert the distance from kilometers to meters:
Given distance = 3.3 km
Convert km to m by multiplying the distance by 1000:
Distance = 3.3 km × 1000 m/km = 3300 m
2. Convert the time from minutes to seconds:
Given time = 2.8 min
Convert min to s by multiplying the time by 60:
Time = 2.8 min × 60 s/min = 168 s
3. Use the equation of motion to calculate the final speed:
The equation of motion for uniformly accelerated motion is:
v = u + at
where,
v = final velocity
u = initial velocity
a = acceleration
t = time
Given:
u = 6.9 m/s (initial velocity)
a = unknown (acceleration)
t = 168 s (time)
Since the car is accelerating uniformly, we can assume its acceleration remains constant throughout the motion.
Using the equation of motion, we can solve for the acceleration:
v = u + at
v = 6.9 m/s + a × 168 s
Now, we need an additional piece of information to determine the acceleration.
Please provide the final speed of the car or any other known information about the acceleration to calculate the final speed.