Question

The position of a particle along the x axis depends on the time according to the equation
x = At2 − Bt3

, where x is in meters and t is in seconds. (a) What SI units must A and B
have? For the following, let their numerical values in SI units be 3.0 and 1.0, respectively. (b)
What time does the particle reach its maximum positive x position? (c)what total path length
does the particle cover in the first 4 seconds?

Answer 1

Answer on Question #70325-Physics-Other

The position of a particle along the x axis depends on the time according to the equation $x = At2 - Bt3$ , where $x$ is in meters and $t$ is in seconds.

(a) What SI units must A and B have? For the following, let their numerical values in SI units be 3.0 and 1.0, respectively.

(b) What time does the particle reach its maximum positive $x$ position?

(c) What total path length does the particle cover in the first 4 seconds?

Solution

a)

$$[ A ] = \frac {m}{s ^ {2}}$$ $$[ B ] = \frac {m}{s ^ {3}}$$

b)

$$\frac {d x}{d t} = 2 A t - 3 B t ^ {2} = 0$$ $$2 A = 3 B t$$ $$t = \frac {2 A}{3 B} = \frac {2}{3} \frac {3}{1} = 2 s.$$

c)

$$X = X (0 < t < 2) + X (2 < t < 4)$$ $$X (0 < t < 2) = 3 (2) ^ {2} - 2 ^ {3} - 0 = 4 m.$$ $$X (2 < t < 4) = | 3 (4) ^ {2} - 4 ^ {3} - 4 | = 2 0 m.$$ $$X = 4 + 2 0 = 2 4 m.$$

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