At time $t$ seconds, where $t > 0$, a particle $P$ moves so that its acceleration $a ext{ ms}^{-2}$ is given by a = (1 - 4t) i + (3 - t) j At the instant when $t = 0$, the velocity of $P$ is $36 ext{ ms}^{-1}$. (a) Find the velocity of $P$ when $t = 4$. (b) Find the value of $t$ at the instant when $P$ is moving in a direction perpendicular to $i$. (ii) At time $t$ seconds, where $t > 0$, a particle $Q$ moves so that its position vector $r$ metres, relative to a fixed origin $O$, is given by r = (t^2 - t) i + 3j Find the value of $t$ at the instant when the speed of $Q$ is $5 ext{ ms}^{-1}$.

A-Level Edexcel Maths Mechanics Working with Vectors: At time $t$ seconds, where $t >

At time $t$ seconds, where $t > 0$, a particle $P$ moves so that its acceleration $a ext{ ms}^{-2}$ is given by a = (1 - 4t) i + (3 - t) j At the instant when $t = 0$, the velocity of $P$ is $36 ext{ ms}^{-1}$ - Edexcel - A-Level Maths Mechanics - Question 3 - 2020 - Paper 1

Question 3

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At time $t$ seconds, where $t > 0$, a particle $P$ moves so that its acceleration $a ext{ ms}^{-2}$ is given by a = (1 - 4t) i + (3 - t) j At the instant when $t ... show full transcript

Worked Solution & Example Answer:At time $t$ seconds, where $t > 0$, a particle $P$ moves so that its acceleration $a ext{ ms}^{-2}$ is given by a = (1 - 4t) i + (3 - t) j At the instant when $t = 0$, the velocity of $P$ is $36 ext{ ms}^{-1}$ - Edexcel - A-Level Maths Mechanics - Question 3 - 2020 - Paper 1

Step 1

Find the value of $t$ at the instant when the speed of $Q$ is $5 ext{ ms}^{-1}$

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Answer

First, we calculate the velocity of $Q$ by differentiating the position vector $r$ with respect to $t$ :

v = \frac{dr}{dt} = (2t - 1)i + 3j.

The speed is given by:

\text{Speed} = \sqrt{(2t - 1)^2 + 3^2}.

Setting the speed equal to 5:

\sqrt{(2t - 1)^2 + 9} = 5\rightarrow (2t - 1)^2 + 9 = 25\rightarrow (2t - 1)^2 = 16\rightarrow 2t - 1 = \pm 4.

This leads to:

$2t - 1 = 4 \Rightarrow t = 2.5$
$2t - 1 = -4 \Rightarrow t = -1.5 \text{ (discarded since } t > 0).$ Thus, the solution is: $t = 2.5$ .

At time $t$ seconds, where $t > 0$, a particle $P$ moves so that its acceleration $a ext{ ms}^{-2}$ is given by a = (1 - 4t) i + (3 - t) j At the instant when $t = 0$, the velocity of $P$ is $36 ext{ ms}^{-1}$ - Edexcel - A-Level Maths Mechanics - Question 3 - 2020 - Paper 1

Find the value of $t$ at the instant when the speed of $Q$ is $5 ext{ ms}^{-1}$

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