For any arbitrary motion in space, which of the following relations are true:
a) `V_"average"` = (1/2) (v (t1) + v (t2))
b) `V_"average"` = [r(t2) - r(t1) ] /(t2 – t1)
c) v (t) = v (0) + a t
d) r (t) = r (0) + v (0) t + (1/2) a t2
e) `a_"average"` = =[ v (t2) - v (t1 )] /( t2 – t1)
(The ‘average’ stands for average of the quantity over the time interval t1 to t2)
(b) and (e) are true; others are false because relations (a), (c) and (d) hold only for uniform acceleration.
(b) and (e)
(a)It is given that the motion of the particle is arbitrary. Therefore, the average velocity of the particle cannot be given by this equation.
(b)The arbitrary motion of the particle can be represented by this equation.
(c)The motion of the particle is arbitrary. The acceleration of the particle may also be non-uniform. Hence, this equation cannot represent the motion of the particle in space.
(d)The motion of the particle is arbitrary; acceleration of the particle may also be non-uniform. Hence, this equation cannot represent the motion of particle in space.
(e)The arbitrary motion of the particle can be represented by this equation.
A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the centre along QO as shown in Fig. If the round trip takes 10 min, what is the (a) net displacement, (b) average velocity, and (c) average speed of the cyclist?
In a harbour, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?
Read each statement below carefully and state, with reasons, if it is true or false:
The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector
- Motion in a Plane