Note: Show all your work to obtain full credit The components of the velocity of

Question

Note: Show all your work to obtain full credit The components of the velocity of an object as function of time are given in the graphs below, when t = 0 s, the object is at position (0,0). 1. V. (m/s) V, (m/s) 50 86.6 5.10 t(s) Calculate: a. When the time is 2 seconds the magnitude and direction of the vector position b. When the time is 1 sec the direction of the vector velocity V c. When the time is 4 sec the magnitude of the vector acceleration a d, when x = 173.2 m, determine the value of the y coordinate e. When t-5.10 sec, determine the direction of the vector velocity V

Explanation / Answer

From the given graph

Vx = 86.6 m/s

Vy = 50 - (50/5.1)t = 50 - 9.80392t

a. hence

dx/dt = Vx

x = Vx*t + C1

x = 86.6t + C1

at t = 0, x = 0

hence

C1 = 0

x = 86.6t

similiarly

y = 50t - 9.80392t^2/2

hence

at t = 2 s

x = 173.2 m

y = 80.39216m

hence

|r| = 190.948 m

direction = arctan(y/x) = 24.89874 deg

b. at t = 1 s

Vx = 86.6 m/s

Vy = 40.19608 m/s

hence

direction = arctan(Vyh/Vx) = 24.8987 deg

c. at t= 4 s

ax = 0

ay = -9.80392 m/s/s

hence a = 9.80392 m/s/s

d. x = 173.2 m

t = 2 s

hence

y = 80.392 m

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