A car is standing 200 m behind a bus , witch is also at rest .The two start moving at same instant but with different forward acceleration. The bus has acceleration 2 m/s^2 and the the car has acceleration 4 m/s^2 .The car will catch up with bus after time of ?
Hello,
The answer to ur question is 14.14
There are 2 ways of solving this question
1st method:
From the frame of reference of bus
The car has a relative acceleration of 2m/s2 towards it
And it had to cover a distance of 200m to reach it so from the frame of reference of bus the equation of motion becomes
S= ut + 1/2*a*t^2
200= 1/2*2*(t)^2
Solving for t u get 14.14
2nd method:
Let the time of interjection of car and bus be t
Let the distance travelled by the bus be x
Then the distance travelled by car is 200+x
From 2nd equation of motion we have
X= 1/2*2*(t)^2..........(i)
X+200= 1/2*4*(t)^2..........(ii)
Subtract (i) from (ii) and solve for t u will get 14.14
Hope this helped
Hello,
So the formula used here is going to be S = u + 1/2 at^2
where s = separation between them = 200 m
u = initial velocity = 0
a = acceleration of car with respect to bus = ( 4-2) m/s^2 = 2 m/s^2
t = time taken by car to catch up to bus = ? (to find)
On Substituting the values in the formula S = u + 1/2 at^2
200 = 0 + 1/2 x (2 x t^2)
200 = 1/2 x 2t^2
200 = t^2
Therefore t = 10 √ 2 Seconds ( 10 root 2 or 10 x 1.414)
Hope this was helpful.
Let it sometime t both car and bus meet
Then the distance travelled by car is 200 more than distance travelled by bus
We know the formula for distance travelled
s=ut+1/2at^2
Therefore
200=(1/2)t^2*(16-4)
t^2=400/12
t=5.77
Therefore car and bus will meet at 5.77 second
VA =Velocity of object A.
VB= Velocity of object B.
Relative velocity of A wr to B is
VAB = VA - VB VAB, VA, V8 All are in same direction.
VBA = VB - VA
Now using these formulas
a) VAB = VA - VB
= (20 - 5) m/s =15m/s
b) VBA=VB - VA
= (5 - 20) m/s =-15m/s
Initial separation between bus and car SCB = 200 meter
Acb = Ac - Ab = 2m/s2 UCB = 0, t =?
Scb= Ucb + (Acb t^2)/2
t^2=200
t=14.14 sec
