#### A graph of x versus t is shown in Fig. 3.3. Choose correct alternatives from below. (a) The particle was released from rest at t = 0. (b) At B, the acceleration a > 0. (c) At C, the velocity and the acceleration vanish. (d) Average velocity for the motion between A and D is positive. (e) The speed at D exceeds that at E.

The correct answer is the option:

(a) The particle was released from rest at t = 0.

(c) At C, the velocity and acceleration vanish.

(e) The speed at D exceeds that at E.

Explanation: Now, we know that,

Slope of the x-t graph gives us

Verification of opt(a)-

is zero or particle is at rest at A since graph (x-t) is parallel to the time axis.

Slope  increases after A and hence velocity also increases.

Verifying option (c) and rejecting opt (b)-

Now,  or v = 0 since the tangent at B & C is graph (x-t), viz., parallel to the time axis. Hence, acceleration = 0.

Verifying opt (e)-

Speed at D is greater than speed at E since the slope at D is greater at D than at E.

Rejecting opt (d)-

Average velocity at A is zero as graph (x-t) is parallel to time axis, also displacement is negative at D, which makes it clear that the velocity at D is also negative.