A car starts from a certain point at a velocity of 100 kph. After 20 seconds, another car staring from rest, starts at the same point following car A at a uniform acceleration of 3 m/s². Assuming that the road is boundless will car B overtake car A? If yes, where and when?
100,000 meters/3600 seconds = 27.8 m/s
d = 27.8 t
d = (1/2)(3)(t-20)^2
so
18.5 t = t^2 -40 t + 400
solve quadratic for t
Sorry Damon. Gives imaginaries.
x = 27.8(t+20)
x = 1/2(3)t^2
1.5t^2=27.8t+556
1.5t^2 - 27.8t - 556 = 0
Real solutions
d = 27.8 * 20 = 556 m. Head
start.
0.5a*t^2 = 556 + 27.8t.
1.5t^2 = 556 + 27.8t.
1.5t^2 - 27.8t - 556 = 0.
t = Time required for B to catchup.
0.5a*t^2 = Distance at which B catches up.
To determine if car B will overtake car A, we need to calculate the positions of both cars at different times and compare them. Let's break down the problem step by step:
1. Determine the position of car A after 20 seconds:
Since car A started with a velocity of 100 km/h and there is no mention of any change in its velocity, we can assume that it will maintain a constant velocity throughout. We can use the formula:
position = initial velocity × time
Convert the velocity of car A to m/s:
100 km/h = 100000 m/3600 s ≈ 27.78 m/s
Now calculate the position of car A after 20 seconds:
position of car A = 27.78 m/s × 20 s = 555.6 m
2. Determine the position of car B after 20 seconds:
Car B starts from rest and uniformly accelerates at 3 m/s². We can use the equation of motion:
position = initial velocity × time + (1/2) × acceleration × time²
Since car B starts from rest, the initial velocity is 0:
position of car B = (1/2) × 3 m/s² × (20 s)² = 600 m
Comparison and conclusion:
After 20 seconds, car A is at 555.6 m and car B is at 600 m. So car B overtakes car A and continues to move ahead. The exact location and time when car B overtakes car A can be calculated by setting their positions equal to each other and solving for time or distance. However, since the road is assumed to be boundless, car B will eventually overtake car A at an infinite distance from the starting point, making it impossible to pinpoint the exact location and time of the overtake.