The velocity of a particle constrained to move along the x-axis as a function of

Question

The velocity of a particle constrained to move along the x-axis as a function of time t is given by:

v(t)=?(19/t0)sin(t/t0).

Part B)

Denote instantaneous acceleration of this particle by a(t). Evaluate the expression 9 +v(0)t+a(0)t2/2 at t = 4t0. Note that v(0)and a(0) are the velocity and acceleration at time t=0.

Part C)

Now assume that the particle is at x=0 when t=0, and find its position at t = 0.20t0.

Part D)

Evaluate v(0)t+a(0)t2/2 at t=0.20t0 to 3 significant figures. Your answers to parts (c) and (d) should be in good agreement. Try to work out why that is so before submitting the answer to part (d)

Explanation / Answer

v(t)=-(19/t0)sin(t/t0).

Part B)

instantaneous acceleration of this particle by a(t)

=dv(t)/dt

=-1.9/t02cos(t/t0).

9 +v(0)t+a(0)t2/2

9-(19/t0)sin(4).*4t0.-1.9/t02cos(4)*16t02

Part C)

9 +v(0)t+a(0)t2/2

t = 0.20t0

9-(19/t0)sin(0.2).*2t0.-1.9/t02cos(0.2)*0.04t02.

Part D)

-(19/t0)sin(0.2).*0.2t0.-1.9/t02cos(0.2)*0.04t02.

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