14. (a) State Newton's second law of motion and show that the first law of motion can be mathematically stated from the mathematical expression for the second law of motion. (b) A stone dropped from a window reaches the ground in 0.5 seconds (given g = 10 ms^-2 ).
i) calculate the speed just before it hits the ground
ii) what is average speed t = 0.5 s ?
iii) calculate the height of window from the ground
NO INCORRECT ANSWERSS
Answers
Initial speed (u) = 0 (as the stone is at rest)
Time = 0.5 seconds
Acceleration = 9.8m/s²
i) According to first equation of motion:
v = u + at
v = 0 + 9.8 x 0.5
v = 4.9 m/s
This is the speed just before stone hits the ground
ii) According to third equation of motion :
v² = u² + 2as
(4.9)² = 0 + 2 x 9.8 x s
24.01 = 19.6s
s = 1.225
so the average speed = 1.225/0.5 = 2.45m/s
iii) Height of window from the ground
Height = 1.225m
Answer:a)The second law of motion states that the rate of change of momentums of an object is proportional to the applied unbalanced force in the direction of force
The first law of motion can be mathematically stated from the mathematical expression for the second law of motion. Eq is
F=ma
or F= m(v-u) / t
or F= mv-mu
That is, when F=0,v=u for whatever time t is taken. This means that the object will continue moving with uniform velocity, u is throughout the time, t. If u is zero then v will also be zero. That is, the object will remain at rest
b)Initial speed (u) = 0 (as the stone is at rest)
Time = 0.5 seconds
Acceleration = 9.8m/s²
i) According to first equation of motion:
v = u + at
v = 0 + 9.8 x 0.5
v = 4.9 m/s
This is the speed just before stone hits the ground
ii) According to third equation of motion :
v² = u² + 2as
(4.9)² = 0 + 2 x 9.8 x s
24.01 = 19.6s
s = 1.225
so the average speed = 1.225/0.5 = 2.45m/s
iii) Height of window from the ground
Height = 1.225m