State whether the following statements are true or false:
(a) The velocity time graph of a particle falling freely under gravity would be a straight line parallel to the axis.
(b) If the velocity- time graph of a particle is a straight line inclined to time axis, then its displacement - time graph will also be a straight line?

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Solution

(a)False,because acceleration=g.But by graph $\frac{d v}{d t} =$ acceleration=0
(b) $\frac{d v}{d t}$ =constant=acceleration
False,displacement-time graph will be parabolic in nature as $s = u t + \frac{1}{2} a t^{2}$ where s is the displacement.

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For uniform motion :

(a) the distance-graph is a straight line parallel to the time axis.

(b) the speed-time graph is a straight line inclined to the time axis.

(d) the acceleration-time graph is a straight line parallel to the time axis.

A object moves with uniform positive acceleration. Its velocity-time graph will be
(a) A straight line parallel to the time axis
(b) A straight line inclined at an obtuse angle to the time axis
(c) A straight line inclined at an acute angle to the time axis
(d) None of these.

Q. The displacement-time graph being a straight line inclined to the time axis implies

Q. Displacement-time graph being a straight line parallel to the time axis implies

Q. The velocity-time graph being a straight line parallel to the velocity axis implies

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(a)False,because acceleration=g.But by graph dvdt=acceleration=0(b)dvdt=constant=accelerationFalse,displacement-time graph will be parabolic in nature as s=ut+12at2 where s is the displacement.

(a)False,because acceleration=g.But by graph $\frac{d v}{d t} =$ acceleration=0
(b) $\frac{d v}{d t}$ =constant=acceleration
False,displacement-time graph will be parabolic in nature as $s = u t + \frac{1}{2} a t^{2}$ where s is the displacement.