The acceleration time diagram for a linear motion is shown. Construct velocity time diagram and displacement time diagram for the motion assuming that the motion starts with a initial velocity of 5 m/s from the starting point.

**Given** : Acceleration time graph**To draw** : Velocity time graph

Displacement time graph

#### Solution

**FOR VELOCITY TIME GRAPH :**

We know that the area under a-t graph gives the velocity.

AB on a-t graph represents linearly varying deceleration

`v_0 = 5 m ⁄ s `

`v_1 = v_0 + A(△ OAB )`

`= 5 + 1/2 xx 6 xx 1`

= 8 m/s

BC on a-t graph represents linearly varying acceleration

`v_2 = v_1 + A(△BCD)`

`=8 + 1/2 xx (12-6) xx 2`

=14 m/s

The velocity time graph is drawn below :

**FOR DISPLACEMENT TIME GRAPH :**

Area under v-t graph gives the displacement

Area under EF = A(EFH) + A(▭EHIO)

`=2/3 xx 6 xx (8-5) + 6 xx 5`

= 42 m

Area under FG = A(GFH) +A(▭FIJK)

`=1/3 xx (12 – 6) xx (14-8) + (12 – 6) xx 8`

=12 + 48

= 60 m

The displacement time graph is shown below :