Edexcel A-Level Mathematics AS M1.3 Kinematics of a Particle Moving in a Straight Line Questions

Straight-line kinematics questions usually turn on choosing the right model: suvat for constant acceleration, graph gradients for acceleration and areas for distance.

Exam points

Choose a suvat equation for time, speed, height or displacement in vertical motion.
Use speed-time graph gradients for acceleration and areas for distance travelled.
Equate displacement expressions when two particles meet or one vehicle catches another.

Covered syllabus points

M1.3.1 - Constant-acceleration motion in a straight line

[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 ]

[Maximum number: 3]

Figure 5

A parcel of mass 2 kg is pulled up a rough inclined plane by the action of a constant force.

The force has magnitude 18 N and acts at an angle of 40^ to the plane.
The line of action of the force lies in a vertical plane containing a line of greatest slope of the inclined plane.

The plane is inclined at an angle of 30^ to the horizontal, as shown in Figure 5.
The coefficient of friction between the plane and the parcel is 0.3
The parcel is modelled as a particle P

The points A and B lie on a line of greatest slope of the plane, where A B=5 m and B is above A. Particle P passes through A with speed 2 ms^-1 in the direction AB.

The force of 18 N is removed at the instant P passes through B. As a result, P comes to rest at the point C.

Find the speed of P as it passes through B.

$v^2=2^2+2(1.18)(5)$
M1 A1ft

$v=3.98\text{ or }4.0\text{ or }4\text{ m s}^{-1}$
A1 cao

N.B. For (a) and (b), penalise over-accurate answers once only.

[Maximum number: 8]

At time t=0, a small ball is projected vertically upwards from a point A which is
24.5 m above the ground. The ball first comes to instantaneous rest at the pointeg B, where $A B=19.6 \mathrm{~m}$ and first hits the ground at time t=T seconds.

The ball is modelled as a particle moving freely under gravity.

(a)

Find the value of T.

[ 6 ]

$0^{2}=u^{2}-2 \times g \times 19.6$ $-24.5=u T-\frac{1}{2} g T^{2}$
Produce an equation in Tonly and solve for T
T=5
(6)

(b)

Sketch a speed-time graph for the motion of the ball from t=0 to t=T seconds.
(No further calculations are needed in order to draw this sketch.)

[ 2 ]

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (c)

Question (d)

Question 2

Question 3

Question (a)

Question (b)