Suppose that a particle moves according to the law of motion v ( t ) = (B) What

Question

Suppose that a particle moves according to the law of motion

v(t)=  
(B) What is the velocity after 3 seconds?

Velocity after 3 seconds =  
(C) Find all values of t for which the particle is at rest. (If there are no such values, enter 0. If there are more than one value, list them separated by commas.)

t =  
(D) Use interval notation to indicate when the particle is moving in the positive direction. (If the particle is never moving in the positive direction, enter "{}" without the quotation marks.)

Answer =  
(E) Find the total distance traveled during the first 8 seconds.

Total distance =  

Explanation / Answer

D) For particle to be moving in the positive x direction

x > 0, which means

4t/(t^2 + 9) > 0

Now t^2 + 9 is always grreater than 0

hence t > 0 for the particle to be always moving in the positive x direction

E) Total Distance traveled in first 8 seconds can be calculated by putting x(8) = 4*8/(64 + 9) = 32/73 = 0.438 m

Hence distance = 0.438 m

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