A) We can use the equation of motion:
2as = v² - u²
s = (12² - (-6)²) / 2 x 4
s = 13.5 m
b) We calculate the time over which this displacement occurred using:
v = u + at
t = (12 - -6)/4
t = 4.5 seconds
Assuming the average speed equal to:
(12 + 6) /2 = 9 m/s
average speed = total distance/total time
total distance = 9 x 4.5
= 40.5 m
Answer: 10 m/2^2
F=ma
Explanation:
Force = 1000N
1 N is 1 (kg*m/s^2)
Mass = 100kg
F=ma
a = F/m
a = (1000kg*m/s^20/(100kg)
a = 10 m/s^2
Answer is D.
Speed:
Use relative speed to simplify the situation. Since the trains are moving in opposite directions, you can add the speeds and pretend the first train is stationary (moving at 0m/s) and the second train is moving at 50m/s.
Distance:
The front of the second train needs to travel 120m to get from the front to the back of the first train. When the front of the second train is at the back of the first train, the back of the second train is still 10m in front of the first train. The back therefore has to travel 130m to clear the first train. The total distance over which the trains are overlapping in this scenario is therefore 120 + 130 = 250m.
You have speed and you have distance so now just calculate time:
v = d / t
50 = 250 / t
t = 5s
The emerging velocity of the bullet is <u>71 m/s.</u>
The bullet of mass <em>m</em> moving with a velocity <em>u</em> has kinetic energy. When it pierces the block of wood, the block exerts a force of friction on the bullet. As the bullet passes through the block, work is done against the resistive forces exerted on the bullet by the block. This results in the reduction of the bullet's kinetic energy. The bullet has a speed <em>v</em> when it emerges from the block.
If the block exerts a resistive force <em>F</em> on the bullet and the thickness of the block is <em>x</em> then, the work done by the resistive force is given by,

This is equal to the change in the bullet's kinetic energy.

If the thickness of the block is reduced by one-half, the bullet emerges out with a velocity v<em>₁.</em>
Assuming the same resistive forces to act on the bullet,

Divide equation (2) by equation (1) and simplify for v<em>₁.</em>

Thus the speed of the bullet is 71 m/s