Answer to Question #301332 in Physics for ezekiel

Question #301332

The distance S in meters covered by a particle at time t seconds is given by

S=2t³-3t²-5t.Find

i) It's speed in the 5th second

ii) It's distance in the 3rd second

iii) The time the particle is momentarily at rest

iv) The acceleration at t=5s?


1
Expert's answer
2022-02-23T08:31:45-0500

Given:

S=2t³3t²5tS=2t³-3t²-5t

i) It's speed in the 5th second

v=S=6t26t5v(5)=652655=115m/sv=S'=6t^2-6t-5\\ v(5)=6*5^2-6*5-5=115\:\rm m/s

ii) It's distance in the 3rd second

S(3)=23333253=12mS(3)=2*3^3-3*3^2-5*3=12\:\rm m

iii) The time the particle is momentarily at rest

v=6t26t5=0v=6t^2-6t-5=0

t=1.54st=1.54\:\rm s

iv) The acceleration at t=5s?

a=v=12t6a(5)=1256=54m/s2a=v'=12t-6\\ a(5)=12*5-6=54\:\rm m/s^2


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