Question

1- if an equation of motion given by ( X=2t , Y=2t+4 ) prove that the motion is Straight.

2- if the position of object given by (
X=3t-4t^{2}+t^{3} )

a- give the position at ( t=1),( t=2 ),( t=3 ),( t=4 )

b- find the displacement between ( t_{1} = 0 and
t_{2} = 4 )

c- find the average velocity between ( t_{1} = 2 and
t_{2} = 4 )

Answer #1

The position (in meters) of an object moving in a straight
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s(t)=√ 3t+1 −2t^2+1
where t is measured in seconds.
(a) Find the average velocity on [0,1].
(b) Find the instantaneous velocity at t=1.
(c) Find the acceleration at t=1.

A Honda Civic travels in a straight line along a road. Its
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equation x(t)= α t2−β t3, where α = 1.52 m/s2 and β =
5.35×10−2 m/s3
Calculate the average velocity of the car for the time interval
t=0 to t1 = 1.95 s .
Calculate the average velocity of the car for the time interval
t=0 to t2 = 4.05 s
Calculate the...

The position of a particle moving with constant acceleration is
given by
x(t) = 4t2 + 3t +
4
where x is in meters and t is in seconds.
(a) Calculate the average velocity of this particle between
t = 2 seconds and t = 7 seconds.
(b) At what time during this interval is the average velocity equal
to the instantaneous velocity?
(c) How does this time compare to the average time for this
interval?
a. It is larger....

Eliminate the parameter to find a Cartesian equation of the
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a) x=3t+2,y=2t−3
b) x=21sin(t)−3,y=2cos(t)+5

Consider the parameterized motion given by
r(t)=3t^2i-2t^2j+(6-t^3)k.
Where is the object at time t=1? What is the velocity at t=1?
What is the speed at t=1?
How far does the object move from 0≤t≤1? Round your
answer to 2 decimal places.
* r, i, j, and k should all have vector arrows above them

1. The position of an object along the x-axis in meters is given
by: x(t) = 1 + 2t + 3t 2 (
a) Plot x(t) as a function of t from t = 0 s to 10 s,
(b) At 2 s, what is position, speed, and acceleration of the
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Find an equation of the normal plane to x = t, y = t2 , z = t3
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the curve shown below has parametric equations : x =
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< infinity).
find the value of t which gives point (10,0) on the curve, and
determine the slope of the curve at this point.

The position of a particle confined to move on an axis varies
according to the equation x(t)=at3 -bt-c where a=2m/s3 , b=4m/s,
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Draw the graph of the motion, then find the following:
a) the average velocity between t1=0 and t2=2s.
b) the instantaneous velocity and acceleration functions,
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Evaluate the line integral, where C is the given
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xyeyz dy, C: x =
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4t2, z =
3t3, 0 ≤ t ≤ 1
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