The position of an object is given by the equation x = 4.0t2 - 2.0 t - 4.5where x is in meters and t is in seconds. What is the
1 answer:
Answer:
j
Explanation:
x = 4 t^2 - 2 t - 4.5
Position at t = 3 s
x = 4 (3)^2 - 2 (3) - 4.5 = 25.5 m
Velocity at t = 3 s
v = dx / dt = 8 t - 2
v ( t = 3 s) = 8 x 3 - 2 = 22 m/s
Acceleration at t = 3 s
a = dv / dt = 8
a ( t = 3 s ) = 8 m/s^2
When is the velocity = 0
v = 0
8 t - 2 = 0
t = 0.25 second
When is the position = 0
x = 0
4 t^2 - 2 t - 4.5 = 0
t = 1.4 second
You might be interested in
Explanation:
Since, the rod is present in vertical position and the spring is unrestrained.
So, initial potential energy stored in the spring is = 0
And, initial potential gravitational potential energy of the rod is .
It is given that,
mass of the bar = 0.795 kg
g = 9.8
L = length of the rod = 0.2 m
Initial total energy T =
Now, when the rod is in horizontal position then final total energy will be as follows.
T =
where, I = moment of inertia of the rod about the end =
Also,
where, = speed of the tip of the rod
x = spring extension
The initial unstrained length is = 0.1 m
Therefore, final length will be calculated as follows.
x' = m
Then, x =
x = m - 0.1 m
= 0.1236 m
k = 25 N/m
So, according to the law of conservation of energy
Putting the given values into the above formula as follows.
v = 2.079 m/s
Thus, we can conclude that tangential speed with which end A strikes the horizontal surface is 2.079 m/s.