Explain why or why not Determine whether the following statementsare true and give an explanation or counterexample.a. If the speed of an object is constant, then its velocity componentsare constant.b. The functions r(t) = ⟨cos t, sin t⟩ and R(t) = ⟨sin t2, cos t2⟩generate the same set of points, for t ≥ 0.c. A velocity vector of variable magnitude cannot have a constantdirection.d. If the acceleration of an object is a(t) = 0, for all t ≥ 0, then the velocity of the object is constant.e. If you double the initial speed of a projectile, its range also doubles (assume no forces other than gravity act on the projectile).f. If you double the initial speed of a projectile, its time of flightalso doubles (assume no forces other than gravity).g. A trajectory with v(t) = a(t) ≠ 0, for all t, is possible.
Explain why or why not Determine whether the following statements
are true and give an explanation or counterexample.
a. If the speed of an object is constant, then its velocity components
are constant.
b. The functions r(t) = ⟨cos t, sin t⟩ and R(t) = ⟨sin t2, cos t2⟩
generate the same set of points, for t ≥ 0.
c. A velocity vector of variable magnitude cannot have a constant
direction.
d. If the acceleration of an object is a(t) = 0, for all t ≥ 0, then the velocity of the object is constant.
e. If you double the initial speed of a projectile, its range also doubles (assume no forces other than gravity act on the projectile).
f. If you double the initial speed of a projectile, its time of flight
also doubles (assume no forces other than gravity).
g. A trajectory with v(t) = a(t) ≠ 0, for all t, is possible.
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