Complete Question
Q. Two go-carts, A and B, race each other around a 1.0km track. Go-cart A travels at a constant speed of 20m/s. Go-cart B accelerates uniformly from rest at a rate of 0.333m/s^2. Which go-cart wins the race and by how much time?
Answer:
Go-cart A is faster
Explanation:
From the question we are told that
The length of the track is 
The speed of A is 
The uniform acceleration of B is 
Generally the time taken by go-cart A is mathematically represented as
=> 
=> 
Generally from kinematic equation we can evaluate the time taken by go-cart B as

given that go-cart B starts from rest u = 0 m/s
So

=>
=>
Comparing
we see that
is smaller so go-cart A is faster
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Answer:

Explanation:
For a linear elastic material Young's modulus is a constant that is given by:

Here, F is the force exerted on an object under tensio, A is the area of the cross-section perpendicular to the applied force,
is the amount by which the length of the object changes and
is the original length of the object. In this case the force is the weight of the mass:

Replacing the given values in Young's modulus formula:

Answer:
(a) r = 1.062·R
= 
(b) r = 
(c) Zero
Explanation:
Here we have escape velocity v
given by
and the maximum height given by

Therefore, when the initial speed is 0.241v
we have
v =
so that;
v² =
v² = 
is then

Which gives
or
r = 1.062·R
(b) Here we have

Therefore we put
in the maximum height equation to get

From which we get
r = 1.32·R
(c) The we have the least initial mechanical energy, ME given by
ME = KE - PE
Where the KE = PE required to leave the earth we have
ME = KE - KE = 0
The least initial mechanical energy to leave the earth is zero.