A particle moves according to the equation x =8.0 t 2 where x is in meters and t

Question

A particle moves according to the equation x =8.0t 2 wherex is in meters and t is in seconds. (a) Find the average velocity for the timeinterval from 1.90 s to 2.90 s.
1 m/s

(b) Find the average velocity for the time interval from1.90 s to 2.00s.
2 m/s

Having problems understanding the setup of the problem
(a) Find the average velocity for the timeinterval from 1.90 s to 2.90 s.
1 m/s

(b) Find the average velocity for the time interval from1.90 s to 2.00s.
2 m/s

Having problems understanding the setup of the problem

Explanation / Answer

The particle moves according to the equation x = 8.0t2 -----------(1) where x is in meters and t is in seconds (a)Differentiating equation (1) with respect to t,wehave (dx/dt) = 8.0 * 2t = 16.0t or v = (dx/dt) = 16.0t When t = 1.90s,then v1 = 16.0 * 1.90 = 30.4 m/s When t = 2.90s,then v2 = 16.0 * 2.90 = 46.4 m/s The average velocity for the time interval from t = 1.90s to t= 2.90s is v = (v1 + v2/2) or v = (30.4 + 46.4/2) = 38.4 m/s (b)When t = 1.90s,then v1 = 16.0 * 1.90 = 30.4 m/s When t = 2.00s,then v2 = 16.0 * 2.00 = 32.0 m/s The average velocity for the time interval from t = 1.90s to t= 2.00s is v = (v1 + v2/2) or v = (30.4 + 32.0/2) = 31.2 m/s where x is in meters and t is in seconds (a)Differentiating equation (1) with respect to t,wehave (dx/dt) = 8.0 * 2t = 16.0t or v = (dx/dt) = 16.0t When t = 1.90s,then v1 = 16.0 * 1.90 = 30.4 m/s When t = 2.90s,then v2 = 16.0 * 2.90 = 46.4 m/s The average velocity for the time interval from t = 1.90s to t= 2.90s is v = (v1 + v2/2) or v = (30.4 + 46.4/2) = 38.4 m/s (b)When t = 1.90s,then v1 = 16.0 * 1.90 = 30.4 m/s When t = 2.00s,then v2 = 16.0 * 2.00 = 32.0 m/s The average velocity for the time interval from t = 1.90s to t= 2.00s is v = (v1 + v2/2) or v = (30.4 + 32.0/2) = 31.2 m/s v1 = 16.0 * 1.90 = 30.4 m/s When t = 2.00s,then v2 = 16.0 * 2.00 = 32.0 m/s The average velocity for the time interval from t = 1.90s to t= 2.00s is v = (v1 + v2/2) or v = (30.4 + 32.0/2) = 31.2 m/s The average velocity for the time interval from t = 1.90s to t= 2.00s is v = (v1 + v2/2) or v = (30.4 + 32.0/2) = 31.2 m/s

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