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A particle P moves with constant acceleration (2i - 5j) m s² - Edexcel - A-Level Maths Mechanics - Question 1 - 2009 - Paper 1

Question 1

A particle P moves with constant acceleration (2i - 5j) m s². At time t = 0, P has speed u m s⁻¹. At time t = 3 s, P has velocity (-6i + j) m s⁻¹. Find the value o... show full transcript

Worked Solution & Example Answer:A particle P moves with constant acceleration (2i - 5j) m s² - Edexcel - A-Level Maths Mechanics - Question 1 - 2009 - Paper 1

Step 1

P has velocity (-6i + j) m s⁻¹.

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Answer

At time t = 3 seconds, we can express the velocity of particle P using the equation of motion:

$v = u + at$

Where:

v = final velocity
u = initial velocity
a = acceleration
t = time

Substituting the known values:

$(-6i + j) = u + 3(2i - 5j)$

Rearranging this gives us:

$u = (-6i + j) - 3(2i - 5j)$

Calculating:

$u = (-6i + j) - (6i - 15j)$
$u = -6i + j - 6i + 15j$
$u = -12i + 16j$

Step 2

Find the value of u.

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Answer

To find the magnitude of u, we use the formula for the magnitude of a vector:

$|u| = ext{sqrt}(u_x^2 + u_y^2)$

Where:

$u_x = -12$ , $u_y = 16$

So:

$|u| = ext{sqrt}((-12)^2 + (16)^2)$
$|u| = ext{sqrt}(144 + 256)$
$|u| = ext{sqrt}(400)$
$|u| = 20$

Thus, the value of u is 20 m s⁻¹.

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