the maximum possible speed a certain car can achieve is 80 m/s (about 180 mph) the car covers a distance of 1km while accelerating up to this speed from rest how fast is the car moving at the halfway point of 500m (the answer is not 40m/s) at what point is the car moving at half of its maximum possible speed
the average speed is 40 m/s
so it takes 25 s to cover the km
the acceleration is 3.2 m/s²
... 80 m/s / 25 s
speed halfway
500 = ½ * 3.2 * t²
... find t and multiply by the acceleration to find the speed
half speed
40 m/s / 3.2 m/s² = 12.5 s
...average speed is 20 m/s
...distance = 20 m/s * 12.5 s
To find the speed of the car at the halfway point and the point where it is moving at half of its maximum possible speed, we need to understand the concept of uniform acceleration.
The distance covered by a car during constant acceleration can be calculated using the equation:
s = ut + 0.5at^2
Where:
s = distance covered
u = initial velocity (zero in this case since the car starts from rest)
t = time taken
a = acceleration
In this case, the car starts from rest and accelerates to a maximum speed of 80 m/s. We are given that the distance covered during this acceleration phase is 1 km (or 1000 m).
First, let's find the time taken for the car to reach its maximum speed. Using the equation:
s = ut + 0.5at^2
1000 = 0 + 0.5at^2
1000 = 0.5a(80)^2
Solving this equation, we find:
a = 0.25 m/s^2
Now, let's find the time it takes to cover the first 500 meters. We can rearrange the equation above as:
s = ut + 0.5at^2
500 = 0 + 0.5(0.25)t^2
Simplifying, we get:
t^2 = 4000
Taking the square root of both sides:
t = sqrt(4000)
t ≈ 63.25 seconds (rounded)
Now we know the time taken to cover the first 500 meters is approximately 63.25 seconds. To find the speed at this point, we can use the equation:
v = u + at
v = 0 + 0.25 * 63.25
v ≈ 15.81 m/s (rounded)
Therefore, the car is moving at approximately 15.81 m/s (not 40 m/s) at the halfway point of 500 m.
To find the point at which the car is moving at half of its maximum possible speed, we need to find the time it takes to reach half of the maximum speed (40 m/s). We can use the equation:
v = u + at
40 = 0 + 0.25t
Solving for t, we find:
t = 160 seconds
The car will reach half of its maximum speed after approximately 160 seconds of constant acceleration.
Note: It's important to keep in mind that these calculations are based on idealized conditions and may not account for external variables such as air resistance, friction, or other factors that could impact the car's acceleration in reality.