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# A-Level Maths | Constant Acceleration
- URL: https://www.a-level-maths-tutor.com/a-level-maths-constant-acceleration/
- Published: 2026-09-12T10:57:26.000Z
- Updated: 2026-09-12T10:57:26.000Z
- Author: Jaisul Naik

Horizontal motion

### Question 1

A particle passes through the point $A$ with speed $35$ ms⁻¹, moving along a straight horizontal path with constant deceleration $0.8$ ms⁻². The particle passes through the point $B$, $15$ s after passing through $A$.

Find the distance $AB$.

Show Answers 

$|AB| = 435$ m

### Question 2

A particle passes through the point $A$ with speed $8$ ms⁻¹, moving along a straight horizontal path with constant acceleration $2$ ms⁻². The particle passes through the point $B$, where $AB = 56.25$ m.

Find the speed of the particle as it passes through $B$.

Show Answers 

$v = 17$ ms⁻¹

### Question 3

The points $A$, $B$ and $C$ lie in that order on a straight road. A car passes through $A$ with speed $11$ ms⁻¹, through $B$ with speed $17$ ms⁻¹, and through $C$ with speed $29$ ms⁻¹. The distance $AB = 28$ m. By modelling the car as a particle:

a) Find the distance $AC$.

b) Find the time it takes the car to travel from $A$ to $C$.

Show Answers 

a) $|AC| = 120$ m

b) $t = 6$ s

Vertical motion

### Question 4

A particle is projected vertically upwards with speed $U$ ms⁻¹ from level horizontal ground. The particle is moving freely under gravity and returns to its starting position $5$ s later.

a) Determine the value of $U$.

b) Calculate the greatest height the particle reaches above the ground.

Show Answers 

a) $U = 24.5$ ms⁻¹

b) $H\_{\\max} = 30.625$ m

### Question 5

A particle is projected vertically downwards from a great height. It hits the ground with speed $28$ ms⁻¹.

Determine the time it took the particle to cover the last $15$ m of its motion.

Show Answers 

$t \\approx 0.598$ s

### Question 6

A particle is projected vertically upwards from a balcony which is $2.48$ m above level horizontal ground. The particle is moving freely under gravity, takes $2.45$ s to reach the highest point in its path, before it strikes the ground with speed $v$ ms⁻¹.

Calculate the value of $v$.

Show Answers 

$v \\approx 25.0$ ms⁻¹

### Question 7

A particle is projected vertically upwards with speed $29$ ms⁻¹ from a balcony which is $h$ m above level horizontal ground. The particle is moving freely under gravity and strikes the ground $6$ s later with speed $v$ ms⁻¹.

a) Calculate the value of $h$.

b) Determine the value of $v$.

Show Answers 

a) $h = 2.4$ m

b) $v = 29.8$ ms⁻¹

### Question 8

A particle is projected vertically upwards from level ground with a speed of $14$ ms⁻¹.

a) Determine the speed of the particle and the distance of the particle from the ground, $0.5$ s after projection.

b) Calculate the total distance travelled by the particle during the first $2$ s of its motion.

Show Answers 

a) $v = 9.1$ ms⁻¹, $d\_{0.5} = 5.775$ m

b) $d\_2 = 11.6$ m

### Question 9

A raindrop falls freely from rest from the top of a cliff. After it has fallen a distance of $40$ m, another raindrop falls freely from rest from the top of the same cliff. The height of the cliff is $80$ m.

Calculate, correct to three significant figures, the distance between the two raindrops at the instant the first raindrop reaches the ground.

Show Answers 

$\\approx 73.1$ m

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