A-Level Maths | Constant Acceleration
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 $AB$.
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$|AB| = 435$ 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 $B$.
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$v = 17$ 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 $C$.
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a) $|AC| = 120$ m
b) $t = 6$ s
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.
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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.
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$t \approx 0.598$ 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 $v$.
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$v \approx 25.0$ 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 $v$.
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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.
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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.
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$\approx 73.1$ m
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