You and your friend decide to race fro your respective houses to school and get

Question

You and your friend decide to race fro your respective houses to school and get front row seats for your Physics lecture. Your friend drives a steady 30 m/s the entire way to school. You have a slower start and end up accelerating the entire way there in order to try to catch up to your friend. Your position at any given time t is described by x_1(t) = [(1/8)(t-1)^2 - 155]m. At what time / do you both have the same speed How far apart are you two at the instant you both have the same speed Assume your friend was at position x_2 = 0 m at time t = 0 s. What is your acceleration What is your friend's acceleration Your friend beats you and arrives at school after driving a total of 3 minutes. How fast are you going at that time How far is the school from you at the instant your friend gets to school Use the figure below to answer the next 2 questions. Find the x and y components for the vector A with a magnitude of 10 and an angle of 35^degree from the horizontal. How would you w

Explanation / Answer

given expression is

x = [(1/8)*(t-1)^2 - 15] m

a)

velocity = dx/dt = (1/4)*(t-1)

(1/4)*(t-1) = 30

t = 120 + 1 = 121 sec (at this time you and your friend have same speed)

b)

distance traveled by your friend (at t = 121 sec) = 30*121 = 3630 m

distance traveled by you = (1/8)*(121 - 1)^2 - 15 = 1785 m

they are (3630 - 1785) = 1845 m apart at t = 121 sec

c)

your friend have constant speed so acceleration of your friend is zero.

acceleration of you = dv/dt = (1/4) m/s^2

d)

speed of you at t = 3min = 180 sec

v = (1/4)*(t-1) = (1/4)*(180-1) = 44.75 m/s

e)

total distance of school = 30*180 = 5400 m

distance travel by you in t=180sec = (1/8)(180-1)^2 - 15 = 3990.125 m

5400 - 3990.125 = 1409.875 m far the school from you

2. a)

x component of vector A = 10*cos35 = 8.19

y component of vector A = 10*sin35 = 5.73

b)

A = 8.19 i + 5.73 j

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