A Motor Car-A Moves With Constant Speed Of 60km/hr; A Car B Starts Chasing Car A After 20minutes The Car A Passed, Where And When Car B Overtaking Car A If Acceleration 10km/hr?
since distance = speed * time, we need at time t hours
60t = 5(t - 1/3)^2
note: 10 km/hr is speed, not acceleration. I used a = 10 km/hr^2
To determine where and when Car B overtakes Car A, we need to calculate the time it takes for Car B to catch up with Car A.
First, let's convert Car A's speed from km/hr to m/s:
Car A's speed = 60 km/hr = (60 * 1000) / 3600 = 16.67 m/s
Now, let's calculate the distance Car A travels in the 20 minutes before Car B starts chasing:
Distance = Speed * Time
Distance = 16.67 m/s * (20 * 60 seconds) = 20,000 meters
Next, let's calculate how long it takes for Car B to catch up with Car A:
We can use the formula: Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2
Car A's initial velocity = 20,000 meters (the distance it traveled in 20 minutes)
Car A's acceleration = 0 (since it is moving with a constant speed)
Let's assume Car B overtakes Car A after t seconds.
Then, the distance traveled by Car B at that time is also 20,000 meters.
20,000 = 0 * t + (1/2) * 10 * t^2
20,000 = 5t^2
t^2 = 20,000 / 5
t^2 = 4,000
t = √4,000
t = 63.25 seconds
Therefore, Car B will overtake Car A after approximately 63.25 seconds.
To determine where Car B overtakes Car A, we can calculate the distance that Car B travels in 63.25 seconds:
Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2
Distance = 0 * 63.25 + (1/2) * 10 * (63.25)^2
Distance = (1/2) * 10 * (63.25^2)
Distance = (1/2) * 10 * 4,006.56
Distance = 20,032.8 meters
So, Car B will overtake Car A at a distance of approximately 20,032.8 meters from the starting point.