Question

At t = 10 s, a particle is moving from left to right with a speed of 5.0 m/s. At t = 20 s, the particle is moving right to left with a speed of 8.0 m/s. Assuming the particle’s acceleration is constant, determine (a) its acceleration, (b) its initial velocity, and (c) the instant when its velocity is zero.

Answer 1

a) a= 0.3 m/s²

b) v₀ = 5 m/s

c) t_f= 0

Step-by-step explanation:

Because acceleration is constant:

a= Δv/Δt =( vf-v₀)/(t_f-t₀) Formula (1)

a: acceleration (m/s²)

vf : final speed (m/s)

v₀ : initial speed (m/s)

t_f : final time (s)

t₀ : initial time (s)

Problem development

a) We apply Formula (1)

a= Δv/Δt = ( vf-v₀)/(t_f-t₀)

`a= (8-5)/(20-10) =(3)/(10) = 0.3 (m)/(s^(2) )`

b) v₀: initial speed (m/s)

v₀ = 5 m/s

c) t_f : final time (s) , vf=0 a= 0.3 m/s²

a= ( vf-v₀)/(t_f-t₀)

0.3= ( 0-3)/(t_f-10)

(t_f-10) (0.3) = -3

0.3t_f+ 3 = -3

t_f= 0