Answer:

Explanation:
Assuming no energy lost, according to the law of conservation of energy, the kinetic energy of the automobile becomes potential energy after the crash:

Here m is the automobile's mass, v is the speed of the car before impact, k is the "bumper" constant and x is the compression of the bumper due to the collision. Solving for v:

Answer:

Explanation:
The heaviside function is defined as:

so we see that the Heaviside function "switches on" when
, and remains switched on when 
If we want our heaviside function to switch on when
, we need the argument to the heaviside function to be 0 when 
Thus we define a function f:

The
term inside the heaviside function makes sure to displace the function 5 units to the right.
Now we just need to add a scale up factor of 240 V, because thats the voltage applied after the heaviside function switches on. (
when
, so it becomes just a 1, which we can safely ignore.)
Therefore our final result is:

I have made a sketch for you, and added it as attachment.
Answer: 3.92 N.
Explanation:
Your box weighs 400g, or 0.4kg. In order to lift it, you need to overcome the force of gravity. F = ma, and acceleration due to gravity is -9.8 m/s^2. So gravity acts on the box with a force of 0.4 kg * -9.8 m/s^2 = -3.92 N. A force of +3.92 N is required to overcome this.
Answer:

Explanation:
As we know that if the object is placed on the inclined plane then the force of friction on the object is counterbalanced by the component of the weight of the object along the inclined plane.
So we can say

now if we increase the inclination of the plane then the component of the weight weight along the inclined plane will increase and hence the friction force will also increase.
As we know that the limiting value or the maximum value of friction force at the static condition is given by


so we have

so we will have

so now we have

so maximum possible angle of the inclined plane is

Answer with Explanation:
We are given that
Distance,r=0.27 m
Tangential speed=v=0.49 m/s
a.Angular speed ,
Using the formula



Time period,
b.Amplitude,A=Distance of small eraser from the center of a turnable =0.27 m
c.Maximum speed,
d.Maximum acceleration=