A particles start from rest and acceleration passing 2 point (A and B)which are 100cm apart in 15seconds if the velocity of the particle at B is three times it velocity at A,find i)the velocity of the particles at A. ii)the accelation. iii) the distance of A from the starting piont.
The language is a bit unclear, but it appears that it takes 15 seconds to travel the 100 cm from A to B. If so,
since velocity
v = at
3at = a(t+15)
t = 15/2 s
Since distance
s = 1/2 at^2,
100 + 1/2 at^2 = 1/2 a(t+15)^2
a = 4/9 cm/s^2
So, we have
v@A = (4/9)(15/2) = 10/3
v@B = (4/9)(45/2) = 10
s@A = 1/2 (4/9)(15/2)^2 = 25/2
s@B = 1/2 (4/9)(45/2)^2 = 225/2
Note that 225/2 = 25/2 + 100 as required
To find the answers to these questions, we will use the equations of motion.
First, let's find the velocity of the particle at A.
i) Velocity at A (vA):
We know that the particle starts from rest, which means its initial velocity (u) is zero.
The equation we can use to find the velocity at A is:
v = u + at
Since the particle starts from rest at A, the equation simplifies to:
vA = 0 + a * tA
We are given the time it takes for the particle to reach A, which is 15 seconds. So, we have:
vA = a * 15
Now, let's find the acceleration.
ii) Acceleration (a):
To find the acceleration, we need to use another equation of motion.
The equation we can use is:
v^2 = u^2 + 2as
Since the particle starts from rest at A, the equation simplifies to:
vA^2 = 0 + 2 * a * s
We are given the distance between A and B, which is 100 cm. So, we have:
vA^2 = 2 * a * 100
With this equation, we can solve for a.
Next, let's find the distance of A from the starting point.
iii) Distance of A from the starting point (sA):
We can use a similar equation of motion to find the distance.
The equation we can use is:
s = ut + (1/2)at^2
Since the particle starts from rest, the equation simplifies to:
sA = (1/2) * a * tA^2
We know the time it takes for the particle to reach A, which is 15 seconds. So, we have:
sA = (1/2) * a * (15^2)
Using the equations mentioned above, we can find the velocity at A, the acceleration, and the distance of A from the starting point.