Question

the displacement in metre of a particle moving along X-axis is given by x (t)=5+20t+10t^2
a) find the position of the particle at t=0s,t=1s,t=2s,and t=3s.
b) find the average velocity between t=1s,and t=2s.​

Answer 1

Given info : the displacement in metre of a particle moving along X-axis is given by

x(t) = 5 + 20t + 10t²

To find :

1. find the position of the particle at t = 0s, 1s , 2s and 3s
2. find the average velocity between t = 1s and t = 2s.

solution :

1. the position of the particle at t = 0,

x(0) = 5 + 20(0) + 10(0)² = 5m

x(1) = 5 + 20(1) + 10(1)² = 5 + 20 + 10 = 35 m

x(2) = 5 + 20(2) + 10(2)² = 5 + 40 + 40 = 85 m

x(3) = 5 + 20(3) + 10(3)² = 5 + 60 + 90 = 155 m

2. average velocity between t = 1s and t = 2s , v_av = [x(2) - x(1)]/(2s - 1s)

= (85 - 35)/1

= 50 m/s

Therefore the average velocity between 1s and 2s is 50 m/s.