A particle travels along a straight line with a velocity

aspifsGak5u 2021-12-20 Answered

A particle travels along a straight line with a velocity of v=(4t3t2)ms, where t is in seconds. Determine the position of the particle when t=4s. s=0 when t=0.

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Expert Answer

Jonathan Burroughs
Answered 2021-12-21 Author has 37 answers
Step 1
We denote positive motion is to the right, measured from the origin O for the particle in t=0
The position as a function of time can be found by integrating v=dsdt with t=0, s=0
ds=vdt
ds=(4t3t2)dt
0sds=0t(4t3t2)dt
s=(2t2t3)
The position at t=4s is then:
s=(2×(4)243)=32m
The negative sign indicates that at t=4 is the particle is a position 32 m left of the initial position.

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Janet Young
Answered 2021-12-22 Author has 32 answers
Step 1
We have
v=4t3t2
We integrate the velocity equation with respect to t
v dv=4t3t2 dt
s=4t dt3t2 dt
s=4[t22]3[t33]+C
s=2t2t3+C
We have s=0, when t=0
0=2(0)2(0)3+C
C=0
s=2t2t3
Step 2
Plugging t=4 in the position equation, we get
s=2t2t3
s=2(4)243
s=3264
s=32units

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