Question:
A particle moving along the x-axis has a position given by x=(24t - 2.0t³)m, where t is measured in s. What is the magnitude of the acceleration of the particle at the instant when its velocity is zero
Answer:
24 m/s
Explanation:
Given:
x=(24t - 2.0t³)m
First find velocity function v(t):
v(t) = ẋ(t) = 24 - 2*3t²
v(t) = ẋ(t) = 24 - 6t²
Find the acceleration function a(t):
a(t) = Ẍ(t) = V(t) = -6*2t
a(t) = Ẍ(t) = V(t) = -12t
At acceleration = 0, take time as T in velocity function.
0 =v(T) = 24 - 6T²
Solve for T
Substitute -2 for t in acceleration function:
a(t) = a(T) = a(-2) = -12(-2) = 24 m/s
Acceleration = 24m/s
Answer: Third option
F = 250w
Explanation:
The impulse can be written as the product of force for the time interval in which it is applied.

You can also write impulse I as the change of the linear momentum of the ball

So:

We want to find the force applied to the ball. We know that
milliseconds = 0.03 seconds
The initial velocity
is zero.
The final speed 
So


We must express the result of the force in terms of the weight of the ball.
We divide the expression between the acceleration of gravity


The answer is the third option
The formula for aluminium chloride will be correctly written as AlCl3.
Aluminium is a metal and in this reaction it is an electron donor. It has three electrons in its outermost shell and it is ready to give out all the three electrons to chlorine. Chlorine is a non metal and is an electron acceptor and it is more than ready to accept electrons from aluminium. But a chlorine atom can only receive only one electron from aluminium because, it already has seven electrons in its outermost shell and it only needs eight electrons in its outermost shell to be stable. To solve this problem, three chlorine atoms will react with one aluminium atom in order to accept all the three electrons from aluminium, hence the chemical formula AlCl3..
Answer:
It's option d - Negative acceleration
Explanation:
- Let's start by demonstrate why <em>it's not option b - Speed : </em>Speed is a scalar quantity so it can not be represented by a vector
- Let's check that <em>the green vectors represent velocity</em> (velocity is a vector quantity, velocity is a direction aware, while speed is just a scalar)
- Now let's show that the circled vectors are acceleration vectors:
Mathematically position X , velocity V and acceleration A are:
and 
Where X, V, A are vectors and
indicates the derivate a of a time is equal to b.
So, this show that acceleration is a rate respect of time of velocity ⇒ When acceleration is positive, velocity increments, when acceleration is negative, velocity decrements.
<em>The above explanation correspond to the motion map shown, getting demonstrated that the answer is D - Negative acceleration </em>