Q1
Answer
A particle has velocity $3t - t^2$. Find the time(s) when it has zero acceleration.
1.5
Q2
Answer
The position of a particle is given by $x = t^3 - 3t^2 + 4t$. Find the time(s) when it has zero acceleration.
1
Q3
Answer
A particle has velocity $2t - 3$. Find the displacement of the particle from its starting point when $t = 4$.
4
Q4
Answer
A particle has acceleration $4t - 5$. Initially, it has velocity $2$. Find the time(s) when it is at rest.
0.5, 2
Q5
Answer
A particle has acceleration $3t - 6$. Initially it has velocity $6$. Find the time(s) when it is at rest.
2
Q6
Answer
A particle has acceleration $3\sqrt{t}$. Initially it has a velocity of $5$. Find the displacement of the particle from its original position when $t = 1$.
5.8
Q7
Answer
A particle has displacement $t^3 - 6t^2 + 9t$. Show that the total distance it travels in the first 5 seconds is $28$.
Q8
Answer
A particle has acceleration $3t + 5$. When $t = 1$, its velocity is $6$ and its displacement is $5$. Find an expression for the displacement of the particle at time $t$.
$\dfrac{1}{2}t^3 + \dfrac{5}{2}t^2 - \dfrac{1}{2}t + \dfrac{5}{2}$
Q9
Answer
Shown below is the velocity time graph of a particle which is made up of a straight line with equation $y = 2x$ and a curve with equation $y = x(4-x)$. Find the total distance travelled by the particle.
$\dfrac{28}{3}$
Q10
Answer
A particle has velocity $4t + 2$. When $t = 2$, its displacement is $10$. A second particle has velocity $2t - 5$. When $t = 3$, its displacement is $4$. Find the time at which the particles have equal displacement. Give your answer to 3 significant figures.
1.42