A body is moving with uniform acceleration covers 100m in the first 10s and 150m in the next 10s. Find the initial velocity of the body.
To find the initial velocity of the body, we can use the equation of motion for uniformly accelerated motion. The equation is given by:
s = ut + (1/2)at^2
Where:
- s is the distance covered
- u is the initial velocity
- t is the time taken
- a is the acceleration
We are given that the body covers 100m in the first 10s and 150m in the next 10s.
For the first 10s:
s = 100m
t = 10s
Using the equation of motion, we can rearrange it to solve for u:
u = (2s - at^2) / (2t)
Substituting the values:
u = (2 * 100m - a * (10s)^2) / (2 * 10s)
For the second 10s:
s = 150m
t = 10s
Again using the equation of motion:
u = (2 * 150m - a * (10s)^2) / (2 * 10s)
Since the body is moving with a uniform acceleration, a remains constant for both calculations.
Now, we have two equations to solve for u. By subtracting the second equation from the first equation, we can eliminate a and solve for u:
((2 * 100m - a * (10s)^2) / (2 * 10s)) - ((2 * 150m - a * (10s)^2) / (2 * 10s)) = 0
Simplifying further:
(200m - a * (10s)^2) - (300m - a * (10s)^2) = 0
-100m = 0
This equation has no solution. Therefore, it is not possible to determine the initial velocity of the body with the given information.
you know that with initial velocity v,
s = vt + 1/2 at^2
Now just find
s(10)-s(0) and
s(20)-s(10)
to find a and v.