The displacement \(x\) metres from the origin at time, \(t\) seconds, of a particle travelling in a straight line is given by \(x=t^3-9 t^2+9 t, \quad t \geqslant 0\) --- 5 WORK AREA LINES (style=lined) --- --- 0 WORK AREA LINES (style=blank) --- --- 6 WORK AREA LINES (style=lined) --- a. \(\text{Particle at origin when}\ \ t=0, t=3.\) b. c. \(a=-6\ \operatorname{m/s^{2}}\) c. \(x=t^3-9 t^2+9 t\) \(v= \dfrac{dx}{dt} = 3 t^2-18 t+9\) \(a= \dfrac{dv}{dt}=6 t-18\) \(\text {When } t=2 \text { : }\) \(a=6 \times 2-18=-6\ \operatorname{m/s^{2}}\)
a.
\(x\)
\(=t^3-9 t^2+9 t\)
\(=t\left(t^2-9 t+9\right)\)
\(=t(t-3)^2\)
\(\text{Particle at origin when}\ \ t=0, t=3.\)
b.
Calculus, 2ADV C1 2019 HSC 8 MC
A particle is moving along a straight line. The graph shows the acceleration of the particle.
For what value of `t` is the velocity `v` a maximum?
- `1`
- `2`
- `3`
- `5`
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.
- What is the initial velocity of the particle? (1 mark)
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- When is the velocity of the particle equal to zero? (1 mark)
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- When is the acceleration of the particle equal to zero? (1 mark)
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Calculus, 2ADV C1 2017 HSC 10 MC
A particle is moving along a straight line.
The graph shows the velocity, `v`, of the particle for time `t >= 0`.
How many times does the particle change direction?
- 1
- 2
- 3
- 4
Show Worked Solution
♦♦♦ Mean mark 33%.
`=>A`
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`.
Which statement describes the motion of the particle at the point `P`?
- The velocity is negative and the acceleration is positive.
- The velocity is negative and the acceleration is negative.
- The velocity is positive and the acceleration is positive.
- The velocity is positive and the acceleration is negative.