Total credits =20 points show detailed calculations and analysis A particle move

Question

Total credits =20 points show detailed calculations and analysis A particle moves along a straight line such that its position is defined by s413m. Determine the (1) The position at time t = 4 seconds (2 points) (2) The speed at time t-4 seconds (3 points) (3) The magnitude of acceleration at time t = 4 seconds ( 5 points) (4) The average velocity during the period of 4 seconds (i.e., ti-0 and t2-4s) (5 points) (5) The average speed during the period of 4 seconds (i.e., ti-0 and t2-4s) (5 points) Solution:

Explanation / Answer

s(t) = t^2 - 4t + 3

1)

at t=4

s(t) = t^2 - 4t + 3

s(4) = 4^2 - 4*4 + 3

s(4) = 16 - 16 + 3

s(4) = 3 m

2)

v(t) = d/dt(s(t))

= d/dt(t^2 - 4t + 3)

= 2t - 4

at t=4 s

v(4) = 2*4 - 4

= 4 m/s

Answer: 4 m/s

3)

a(t) = d/dt(v(t))

= d/dt(2t - 4)

= 2 m/s^2

This is true for all time

Answer: 2 m/s^2

4)

s(4) = 3 m

s(0) = 0^2 - 4*0 + 3

= 3 m

average velocity = (s(4) - s(0))/time

= (3 - 3) m / 4 s

= 0 m/s

Answer: 0 m/s

only 4 parts at a time

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