A particle is moving along a straight line such that its pos

A particle is moving along a straight line such that its position from a fixed point is s = (12 -20t^2 + 8t^3) m, where t is in seconds. Determine the total distance traveled by the particle from t = 1 s to t = 4. Also, find the average speed of the particle during this time interval. S_Tot = V_AVG =

Solution

Given equation is a straight line  

S = 12 - 20 t² + 8t³

At t = 1 sec

S₁ = 12 - 20 * 1² + 8 * 1³

S₁ = 0 m

At t = 4 sec

S₄ = 12 - 20 * 4² + 8 * 4³

S₄ = 204 m

S_total = S₄ - S₁ = 204 - 0

S_total = 204 m

Average speed = S_total / time interval   

Average speed = 204 / (4-1)

Average speed = 68 m/s