Question

A particle's position coordinates (x, y) are (1.0 m, 3.0 m) at t = 0; (5.0 m, 5.0 m) at t = 2.0 s; and (14.0 m, 12.0 m) at t = 5.0 s. (a) Find the magnitude of the average velocity from t = 0 to t = 2 s. (b) Find the magnitude of the average velocity from t = 0 to t = 5 s.

Answer 1

a) Magnitude of the average velocity from t = 0 to t = 2 s = 2.24 m/s

b) Magnitude of the average velocity from t = 0 to t = 5 s = 3.16 m/s

Step-by-step explanation:

a) Velocity is rate of change of position.

A particle's position coordinates (x, y) are (1.0 m, 3.0 m) at t = 0

A particle's position coordinates (x, y) are (5.0 m, 5.0 m) at t = 2.0 s

Displacement = (5-1)i + (5-3)j = 4i + 2j

Change in time = 2s

Velocity

`v=(4i+2j)/(2)=2i+j`

Magnitude of velocity

`v=√(2^2+1^2)=2.24m/s`

b) Velocity is rate of change of position.

A particle's position coordinates (x, y) are (1.0 m, 3.0 m) at t = 0

A particle's position coordinates (x, y) are (14.0 m, 12.0 m) at t = 5.0 s

Displacement = (14-1)i + (12-3)j = 13i + 9j

Change in time = 5s

Velocity

`v=(13i+9j)/(5)=2.6i+1.8j`

Magnitude of velocity

`v=√(2.6^2+1.8^2)=3.16m/s`