Suppose that the position vector for a particle is given as r= xi + yj, with x =

Question

Suppose that the position vector for a particle is given as r= xi + yj, with x = at + b and y = ct^2 + d, where a = 1.00 m/s, b= 1.00m, c = .125m/s^2, and d = 1.00m. a.) Calculate the average velocity during the time intervalfrom t = 2.00s to t = 4.00s. b.) Determine the velocity and the speed at t = 2.00s. Answers are given, just need to know how to get to them a.) V = 1.00i + .750j m/s b.)V(2.00s) = 1.00i + .500j m/s; Speed = 1.12m/s Please show work for full points. Suppose that the position vector for a particle is given as r= xi + yj, with x = at + b and y = ct^2 + d, where a = 1.00 m/s, b= 1.00m, c = .125m/s^2, and d = 1.00m. a.) Calculate the average velocity during the time intervalfrom t = 2.00s to t = 4.00s. b.) Determine the velocity and the speed at t = 2.00s. Answers are given, just need to know how to get to them a.) V = 1.00i + .750j m/s b.)V(2.00s) = 1.00i + .500j m/s; Speed = 1.12m/s Please show work for full points.

Explanation / Answer

Since r = xi + yj, with x = at + b and y = ct 2 +d, where a = 1.00 m/s, b = 1.00m, c = .125m/s^2, and d =1.00m we have r = (at + b)i + (ct 2 + d)j r (t) = (t + 1)i + (0.125t 2 + 1)j Velocity v(t) is v(t) = dr(t) /dt v(t) = 1.00i + 0.25tj . a.) Calculate the average velocity during the time intervalfrom t = 2.00s to t = 4.00s. Vavg= (V2 +V1)/2 V1=v (2) = i + 0.5j V2=v (4) = i + 1j Vavg= (2i + 1.5j)/2 Vavg= i + 0.750j . . b.) Determine the velocity and the speed at t = 2.00s. v (2) = 1.00 i + 0.50j V= ( 1 + 0.5 2)= 1.12m/s

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