Edexcel IAL Maths M1.3.1 Kinematics

[Maximum number: 12]

A particle is projected vertically upwards from a point A with speed $24 \mathrm{~m} \mathrm{~s}^{-1}$

The point A is 2.5 m vertically above the point B.
Point B lies on horizontal ground.
The particle moves freely under gravity until it hits the ground at B with speed $V \mathrm{~m} \mathrm{~s}^{-1}$ After hitting the ground the particle does not rebound.

(a)

A to $B: \quad V^{2}=24^{2}+2(-g)(-2.5)$

M1 A1

OR: e.g. $0=24^{2}-2 g h$ and $V^{2}=2 g(h+2.5)$ oe

V=25

A1

(3)

(a)

Find the value of V.

[ 3 ]

A to $B: \quad V^{2}=24^{2}+2(-g)(-2.5)$
OR: e.g. $0=24^{2}-2 g h$ and $V^{2}=2 g(h+2.5)$ oe

V=25
(3)

(b)

Find the time taken for the particle to reach B.

The point C is 10 m vertically above A.

[ 3 ]

Some possible equations in t:
$\begin{aligned} 25&=-24+gt\\ 2.5&=\frac{(25+(-24))t}{2}\\ 2.5&=-24t+\frac12gt^2\\ 2.5&=25t-\frac12gt^2 \end{aligned}$
Or find $t_{\mathrm{UP}}=\frac{24}{g}$ and $t_{\mathrm{DOWN}}=\frac{25}{g}$ , then add.
$t=5\text{ s}$
(3)

(c)

Find the length of time for which the particle is above C.

[ 4 ]

From A to $C: 10=24 t+\frac{1}{2}(-g) t^{2}$
Complete method to find the required time: e.g. solving the above quadratic and finding the positive difference in the roots

N.B. Allow this mark if they solve their quadratic, and give the answer as a range of values: $t_{1},, t_{,,} t_{2}$
4, 4.0 or 3.98 (s)
ALT 1: From A to $C: W^{2}=24^{2}-2 \times 10 g$ $0=W-g\left(\frac{1}{2} t\right)$
4.0 or 3.98 (s)
ALT 2: From A to $C: W^{2}=24^{2}-2 \times 10 g$ $0=W t+\frac{1}{2}(-g) t^{2}$
4.0 or 3.98 (s)
(4)

(d)

Sketch a speed-time graph for the motion of the particle from projection to the instant that it reaches B. (No further calculations are required.)

[ 2 ]

Edexcel A-Level Mathematics AS M1.3.1 Constant Acceleration Motion in a Straight Line Questions

Exam points

Edexcel A-Level Mathematics AS M1.3.1 Constant Acceleration Motion in a Straight Line Questions question 1

Question (a)

Question (b)

Question (c)

Question (d)