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the position of an object in one dimension is given by X(t)=A+Bt+Ct^2, where x is in...

the position of an object in one dimension is given by X(t)=A+Bt+Ct^2, where x is in meters and t is in seconds. find the velocity and acceleration at 3 seconds. what are the units for A, B, and C?
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Answer #1

we have X(t)=A+Bt+Ct2

we know that v=dx/dt

on intergration we get v= B+2Ct

so at time t= 3s

v=B+2C*3

v= B+6C

acceleration = dv/dt

=B+2Ct

a=2C ( acceleration is constant)

from the concept of dimentional analysis,

the dimension of each term on the left hand side =the dimension of each term on right hand side of the unit

dimension of left hand side = m

x= A

so dimension of A = m

again x= Bt

B=x/t=m/s

again

x= Ct2

C=x/t2

C= m/s2

so dimensions of A=m. B=m/s and C=m/s2

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