The position of a particle moving along the x axis depends on the time according

Question

The position of a particle moving along the x axis depends on the time according to the equation x = ct2 bt3, where x is in meters and t in seconds. (a) What are the units of constant c? s2/m s/m2 m2/s m/s2 Correct: Your answer is correct. (b) What are the units of constant b? m/s3 m3/s s3/m s/m3 Correct: Your answer is correct. For the following, let the numerical values of c and b be 6.5 and 1.8, respectively. (For vector quantities, indicate direction with the sign of your answer.) (c) At what time does the particle reach its maximum positive x position? s

Explanation / Answer

a)  The units of c should be m/s^2, because when multiplying with s^2, this give m. So m/s^2  is the correct answer.

b)   The units of b should be m/ s^3, because that multiplied with s^3 gives m. So m/ s^3 is the correct answer.

c) The maximum displacement occurs when dx/dt = 0. Physically this means that the velocity is zero, which signifies a turning point. dx/dt=0 means 2c t - 3 b t^2 = 0. [differentiat dx/dt i.e x = ct2 bt3]

That occurs when t= 0 ( at the starting point) and

when t= 2c/(3b)= 13m/s^2 /(5.4 m/s^3)= 2.4 s

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