The following equations give the position …
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The following equations give the position component, x(t), along the x axis of a particle's motion in four situations (in each equation, x is in meters, t is in seconds, and t > 0): (1) x = (3 m/s)t – (2 m);
(2) x = (–4 m/s2)t2 – (2 m); (3) x = (–4 m/s2)t2;
(4) x = –2 m.
• (a) In which situations is the velocity of the particle constant?
• (b) In which is the vector pointing in the negative x direction?
Posted by Karan Kishore Dv 6 years, 7 months ago
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Pranav Gupta 6 years, 7 months ago
(a) differentiate the functions (1) d(x)/dt = 3m/s (2) d(x)/dt = -(4m/s2)*t (3) d(x)/dt = -(4m/s2)*t (4) d(x)/dt = 0
In (2) & (3) velocity is a function of time, so it will not be constant. But in (1) & (4) velocity is constant, although in (4) it is 0.
(b) The direction of vector depends on slope of the function. In (a) we have found slopes of these functions. (slope of x-t graph = velocity). In (2) & (3) velocity is negative so these vectors will point in negative x direction. But in (1) & (4) velocity is non-negative so it will not point in negative x direction.
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