Answers SerFPSE9 2.P020 WI n object moves along the x axis according to the equa

Question

Answers SerFPSE9 2.P020 WI n object moves along the x axis according to the equation x 3.75t -2.0ot + 3.00, where x is in meters and t is in econds. a) Determine the average speed between t 1.80 s and t 3.80 s. peed is the distance traveled divided by the time. Is the distance traveled equal to the displaceme Enter a number. this case? m/s (b) Determine the instantaneous speed at t - 1.80 s We are given an explicit expression for x as a function of time. Calculus methods can be used to determine the velocity as a function of time. m/s Determine the instantaneous speed at t 3.80 s We are given an explicit expression for x as a function of time. Calculus methods can be used to determine the velocity as a function of time. m/s

Explanation / Answer

A.

Average speed is given by:

V_avg = dX/dt

V_avg = (Xf - Xi)/(tf - ti)

tf - ti = 3.80 - 1.80 = 2.00 sec

X(t) = 3.75t^2 - 2.00*t + 3.00

X(1.80) = 3.75*1.80^2 - 2.00*1.80 + 3.00 = 11.55 m

X(3.80) = 3.75*3.80^2 - 2.00*3.80 + 3.00 = 49.55 m

So,

V_avg = (49.55 - 11.55)/2.00

V_avg = 19.0 m/sec

B.

Instantaneous speed is given by

V = dX/dt

V = d(3.75t^2 - 2.00*t + 3.00)/dt

V = 2*3.75*t - 2*1 + 0

V = 7.5*t - 2

At t = 1.80 sec

V(1.80) = 7.5*1.80 - 2 = 11.5 m/sec

C.

V(3.80) = 7.5*3.80 - 2 = 26.5 m/sec

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