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Calculus, 2ADV C1 2008 HSC 6b

The graph shows the velocity of a particle,  `v`  metres per second, as a function of time,  `t`  seconds.

  1. What is the initial velocity of the particle?   (1 mark)

  2. When is the velocity of the particle equal to zero?    (1 mark)

  3. When is the acceleration of the particle equal to zero?    (1 mark)

Show Answers Only
  1. `20\ text(m/s)`
  2. `t=10\ text(seconds)`
  3. `t=6\ text(seconds)`
Show Worked Solution

i.    `text(Find)\   v  \ text(when)  t=0`

`v=20\ \ text(m/s)`
 

ii.    `text(Particle comes to rest at)\  t=10\ text{seconds  (from graph)}`

 

iii.  `text(Acceleration is zero when)\ t=6\ text{seconds  (from graph)}`

Calculus, 2ADV C1 2014 HSC 9 MC

The graph shows the displacement  `x`  of a particle moving along a straight line as a function of time  `t`.

2014 9 mc

 Which statement describes the motion of the particle at the point  `P`? 

  1. The velocity is negative and the acceleration is positive.
  2. The velocity is negative and the acceleration is negative.
  3. The velocity is positive and the acceleration is positive.
  4. The velocity is positive and the acceleration is negative.
Show Answers Only

`A`

Show Worked Solution

`text(At)\ P,\ text(the particle is moving back towards)\ O`

`text{after hitting a max (positive) displacement}`

`:.\ text(Velocity is negative.)`

`text(Its displacement hits a minimum just after)\ P`

`text(and increases again.)`

`:.\ text{Acceleration is working against (negative) velocity}`

`text(and must be positive.)`

`=>  A`