3.28 The velocity-time graph of a particle in one-dimensional motion is shown in Fig 3.29 :

Which of the following formulae are correct for describing the motion of the particle

over the time-interval t₁ to t₂:

(a) x(t₂ ) = x(t₁) + v (t₁) (t₂ – t₁) +(½) a (t₂ – t₁)²

(b) v(t₂ ) = v(t₁) + a (t₂ – t₁)

(c) v_average = (x(t₂) – x(t₁))/(t₂ – t₁)

(d) a_average = (v(t₂) – v(t₁))/(t₂ – _t1)

(e) x(t₂ ) = x(t₁) + v_average (t₂ – t₁) + (½) a_average (t₂ – t₁)²

(f) x(t₂ ) – x(t₁) = area under the v-t curve bounded by the t-axis and the dotted line

shown.

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:
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