Answer:
v=8m/s
Explanation
The initial velocity, u, of the car=32m/s
Since the car has decelerated, we negate the acceleration
This implies that,
Time,t=4s
Let v be the final velocity,
using the relation,
We obtain the below by substitution
By cross multiplying we obtain,
v=8m/s
Answer:
Half life of the sample,
Given:
Initial amount, N = 1679
Final count of amount, N' = 1336
Time elapsed, t = 4 min = 240 s
Solution:
Now, To calculate the half life, using the relation:
Now, substituting the given values in the above mentioned formula:
Taking log on both the sides:
ln(0.796) = \frac{4}{t_{\frac{1}{2}}}ln(0.5)
(a) 3.5 Hz
The angular frequency in a spring-mass system is given by
where
k is the spring constant
m is the mass
Here in this problem we have
k = 160 N/m
m = 0.340 kg
So the angular frequency is
And the frequency of the motion instead is given by:
(b) 0.021 m
The block is oscillating up and down together with the upper end of the spring. The block will lose contact with the spring when the direction of motion of the spring changes: this occurs when the spring is at maximum displacement, so at
x = A
where A is the amplitude of the motion.
The maximum displacement is given by Hook's law:
where
F is the force applied initially to the spring, so it is equal to the weight of the block:
k = 160 N/m is the spring constant
Solving for A, we find