Car A starts from rest at t = 0 and travels along a straight road with a constant
acceleration of 2 m/s2 until it reaches a speed of 27 m/s. Afterwards it maintains this
speed. Also, when t = 0, car B located 2000 m down the road is traveling towards A at a
constant speed of 20 m/s. Determine the distance traveled by car A when they pass each
other.
for car A
initial velocity u=0m/sec
acceleration=a=2m/s2
speed attained by A =27 m/sec
time taken by A to attain the speed =t
t=[v-u]/a=[27-0]/2=13.5m/sec2
distance traveled by car A in this time =s=ut+1/2at2
s= 0+0.5*2*13.5^2=182.25m
in this time distance traveled by B towards A=27*20/2=270m
so distance remaining between A and B after 27/2sec=2000-[182.25+270]=1547.75m
relative speed between A and B=27-[-20]=47m/sec
as they are moving in opposite direction.
now time taken by A to cross B =1547.75/47=33sec
in this time distance traveled by A=27*33=891m
hence the distances traveled by car A when they pass each
other=182.25+891=1073.25 m
Two cars are traveling along a straight road. Car a maintains a constant speed of 89 km/hr and car b maintains a constant speed of 119 km/hr. at t=0 car b is behind 38km from car a. How far will car a travel from t =0 before it is overtaken by car b. how long from t=0 will it take for this to happen
Well, it seems like Car A is really eager to show off its acceleration skills. It starts from rest and accelerates at a constant rate of 2 m/s^2 until it reaches a speed of 27 m/s. On the other hand, Car B is just cruising at a constant speed of 20 m/s, probably enjoying some relaxing music.
Now, when will these two cars meet? Let's find out!
To start, let's figure out how long it takes Car A to reach a speed of 27 m/s. We can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken. Since u = 0 (Car A starts from rest), v = 27 m/s, and a = 2 m/s^2, we can solve the equation for t.
27 = 0 + 2t
t = 27/2
t = 13.5 seconds
So, it takes Car A 13.5 seconds to reach a speed of 27 m/s.
Now, let's find out how far Car A travels during this time. We can use the formula s = ut + (1/2)at^2, where s is the distance, u is the initial velocity, a is the acceleration, and t is the time taken. Since u = 0 (Car A starts from rest), a = 2 m/s^2, and t = 13.5 seconds, we can solve the equation for s.
s = 0(13.5) + (1/2)(2)(13.5^2)
s = (1/2)(2)(13.5^2)
s = 182.25 meters
So, Car A travels a distance of 182.25 meters during the 13.5 seconds it takes to reach a speed of 27 m/s.
Now, let's figure out when Car A and Car B will meet. Since Car B is already 2000 meters down the road, we can consider their relative positions. Car A needs to catch up to Car B.
During the time it takes for Car A to reach a speed of 27 m/s (13.5 seconds), Car B travels a distance of 20 m/s * 13.5 s = 270 meters.
So, Car A needs to cover 2000 meters (the initial separation) + 270 meters (the distance Car B traveled) = 2270 meters.
To summarize, Car A will travel a distance of 2270 meters when they pass each other.
And there you have it! Car A might be a bit late for the meeting, but at least it showed off its acceleration skills along the way.
To determine the distance traveled by car A when it passes car B, we need to find the time it takes for them to meet. We can set up equations for both cars and solve for the time.
Let's start with car A:
We know that car A starts from rest and has a constant acceleration of 2 m/s^2. We also know that it reaches a speed of 27 m/s.
Using the equation of motion, v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can rearrange the equation to solve for time (t):
27 m/s = 0 + 2 m/s^2 * t
Solving for t, we get:
t = 27 m/s / 2 m/s^2
t = 13.5 s
Now, let's move on to car B:
We know that car B is located 2000 m down the road and is traveling towards car A at a constant speed of 20 m/s. Since both cars are moving in opposite directions, we can consider their relative velocities.
The relative velocity of car B with respect to car A is the sum of their speeds:
Relative velocity = 20 m/s + 27 m/s
Relative velocity = 47 m/s
Now that we have the relative velocity and the time it takes for car A to reach its speed, we can calculate the distance traveled by car A when they pass each other.
Distance = Relative velocity * Time
Distance = 47 m/s * 13.5 s
Distance = 635.5 m
Therefore, car A will travel a distance of 635.5 meters when they pass each other.