A particle\'s position is given by x = 5 - 10t + 2t^2 (where t is in seconds and

Question

A particle's position is given by x = 5 - 10t + 2t^2 (where t is in seconds and x is in meters). (a) what is its velocity at t = 1 s? (Indicate the direction with the sign of your answer.) m/s (b) Is it moving in the positive or negative direction of x just then? positive negative neither (c) What is its speed just then? m/s (d) Is the speed increasing or decreasing just then? increasing decreasing neither (Try answering the next two questions without further calculation.) (e) Is there ever an instant when the velocity is zero? If so, give the time t: if not, enter NONE. S (f) Is there a time after t = 3.5 s when the particle is moving in the negative direction of x? If so, give the time t: if not, enter NONE. S

Explanation / Answer

x= 5-10t+2t^2

v= dx/dt = -10 + 4t

a)v (t=1) = -6 m/s

b)-ve direction

c)6 m/s

d)increasing

e) v = 0 at t= 2.5 seconds

f) no

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