A-Level CAIE Mathematics AS 4.2 Kinematics of motion in a straight line Question Bank

A car starts from rest and moves in a straight line with constant acceleration for a distance of 200 m , reaching a speed of $25 \mathrm{~m} \mathrm{~s}^{-1}$. The car then travels at this speed for 400 m , before decelerating uniformly to rest over a period of 5 s .

A tram starts from rest and moves with uniform acceleration for 20 s . The tram then travels at a constant speed, $V \mathrm{~m} \mathrm{~s}^{-1}$, for 170 s before being brought to rest with a uniform deceleration of magnitude twice that of the acceleration. The total distance travelled by the tram is 2.775 km .

A particle moves in a straight line. The displacement of the particle at time $t \mathrm{~s}$ is $s \mathrm{~m}$, where

Find the velocity of the particle at the instant when its acceleration is zero.

A bus moves in a straight line between two bus stops. The bus starts from rest and accelerates at $2.1 \mathrm{~m} \mathrm{~s}^{-2}$ for 5 s . The bus then travels for 24 s at constant speed and finally slows down, with a constant deceleration, stopping in a further 6 s . Sketch a velocity-time graph for the motion and hence find the distance between the two bus stops.

The diagram shows the velocity-time graph for a train which travels from rest at one station to rest at the next station. The graph consists of three straight line segments. The distance between the two stations is 9040 m .

A particle P is projected vertically upwards with speed $24 \mathrm{~m} \mathrm{~s}^{-1}$ from a point 5 m above ground level. Find the time from projection until P reaches the ground.

A lift moves upwards from rest and accelerates at $0.9 \mathrm{~m} \mathrm{~s}^{-2}$ for 3 s . The lift then travels for 6 s at constant speed and finally slows down, with a constant deceleration, stopping in a further 4 s .

A particle P is projected vertically upwards with speed $11 \mathrm{~ms}^{-1}$ from a point on horizontal ground. At the same instant a particle Q is released from rest at a point $h \mathrm{~m}$ above the ground. P and Q hit the ground at the same instant, when Q has speed $V \mathrm{~m} \mathrm{~s}^{-1}$.

A particle moves up a line of greatest slope of a rough plane inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha=0.28$. The coefficient of friction between the particle and the plane is $\frac{1}{3}$.

An object is released from rest at a height of 125 m above horizontal ground and falls freely under gravity, hitting a moving target P. The target P is moving on the ground in a straight line, with constant acceleration $0.8 \mathrm{~m} \mathrm{~s}^{-2}$. At the instant the object is released P passes through a point O with speed $5 \mathrm{~m} \mathrm{~s}^{-1}$. Find the distance from O to the point where P is hit by the object.