Question

A particle is moving along the x-axis. Its position as a function of time is given as

𝑥 = 𝑏𝑡 − 𝑐𝑡²

.

a) What must be the units of the constants b and c, if x is in meters and t in seconds?

b) At time zero the particle is at the origin. At what later time t does it pass the origin again?

c) Derive an expression for the x- component of velocity.

d) At what time t is the particle momentarily at rest?

e) Derive an expression for the x-component of the particle’s acceleration, ax.

Answer 1

Given:

$$𝑥 = 𝑏𝑡 − 𝑐𝑡^2$$

a)

$$[b]={\rm m/s},\quad [c]={\rm m/s^2}$$

b)

$$𝑥 = 𝑏𝑡 − 𝑐𝑡^2=0$$

$$t_1=0,\quad t_2=b/c$$

c)

$$v_x=x'=b-2ct$$

d)

$$b-2ct=0$$

$$t_3=b/(2c)$$

e)

$$a_x=v_x'=-2c$$