For the one-dimensional motion, described by x = t–sint

(a) x (t) > 0 for all t > 0.

(b) v (t) > 0 for all t > 0.

(c) a (t) > 0 for all t > 0.

(d) v (t) lies between 0 and 2.

Two trains 101 m and 99 m in length are running in opposite direction with velocities 54 km/h and 36 km/h. In what time they will completely cross each other?

Distance travelled by a particle starting form rest and moving with an acceleration of 4/3ms^-2 in the second is

Match List – I with List – II :

List – I                                                                               List – II

(a) h (Planck’s constant)                                               (i) $\left[ML{T}^{-1}\right]$  

(b) E (kinetic energy)                                                     (ii) $\left[M{L}^2{T}^{-1}\right]$        

(c) V (electric potential)                                                (iii) $\left[M{L}^2{T}^{-2}\right]$  

(d) P (linear momentum)                                             (iv) $\left[M{L}^2{I}^{-1}{T}^{-3}\right]$  

Choose the correct answer from the options given below:

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s, the distance travelled by the toy in the next t s will be:

A vehicle travels half the distance with speed  $\mathrm{v}$ and the remaining distance with speed $2\mathrm{v}$ . Its average speed is: