A particle moves along the x axis according to the equation x = 2.05 + 2.94t - t2, where x is in meters and t?

Question

A particle moves along the x axis according to the equation x = 2.05 + 2.94t - t2, where x is in meters and t is in seconds.
(a) At t = 2.80 s, find the position of the particle.
m
(b) What is its velocity?
m/s
(c) What is its acceleration?
m/s2

Answer 1

x=2.05+2.94(2.80)- (2.80)(2.80)
= 2.442m
v=x/t = 2.94-2(2.80)=-2.96m/s it means deccelarates
a=v/t = -2m/s2

Answer 2

(a) Plug 'n chug. Substitute 2.8 for t and evaluate x
(b) Take the 1'st derivative, substitute 2.8 for t and evaluate dx/dt
(c) Take the 2'nd derivative, substitute 2.8 for t and evaluate d²x/dt²

If you've gotten this far into a Calculus or Physics class and haven't learned how to take derivatives and do simple plug 'n chug, you need to go back and start over.

Doug

Answer 3

a) simply plug 2.8 in wherever these is a t and evaluate the resulting equation.

b) differentiate wrt x to obtain velocity = 2.94 -2t and plug in 2.8 wherever you find t and that is the velocity.

c) differentiate again wrt x to get acceleration = -2m/s^2