Year 11 Maths - Specialist Kinematics

Velocity–Time Graphs

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Questions

Question 1

58022

A particle starts from rest and accelerates uniformly for $4s$ until it reaches a speed of $8\,m/s$. It immediately decelerates uniformly until it comes to rest after a further $6s$. How far did it travel?

Answer

$40m$

Worked Solution

$$
\begin{aligned}
V&=u+a t \\
u&=0, v=8, t=4 \\
8&=0+4 a \\
\therefore\ & a=2 \\
v&=2 t \\
D_{1}&=\frac{1}{2} \times 4 \times 2 \times 4 \\
&=16 m\\
D_{2}&=\frac{1}{2} \times 6 \times 8 \\
&=24 \\ \text { Total distance } &=16+24 \\
&=40 \mathrm{~m}
\end{aligned}
$$

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