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)
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
The position of a particle is given by
`r = 3.0t hati − 2.0t 2 hatj + 4.0 hatk m`
Where t is in seconds and the coefficients have the proper units for r to be in metres.
(a) Find the v and a of the particle?
(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s?
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?