A-Level CAIE Mathematics A2 4.2 Kinematics of motion in a straight line Question Bank

The diagram shows a velocity-time graph which models the motion of a car. The graph consists of six straight line segments. The car accelerates from rest to a speed of $20 \mathrm{~m} \mathrm{~s}^{-1}$ over a period of 5 s , and then travels at this speed for a further 20 s . The car then decelerates to a speed of $6 \mathrm{~m} \mathrm{~s}^{-1}$ over a period of 5 s . This speed is maintained for a further (T-30) s. The car then accelerates again to a speed of $20 \mathrm{~m} \mathrm{~s}^{-1}$ over a period of (50-T) s, before decelerating to rest over a period of 10 s .

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.

One end of a light inextensible string is attached to a block. The string makes an angle of $60^{\circ}$ above the horizontal and is used to pull the block in a straight line on a horizontal floor with acceleration $0.5 \mathrm{~m} \mathrm{~s}^{-2}$. The tension in the string is 8 N . The block starts to move with speed $0.3 \mathrm{~m} \mathrm{~s}^{-1}$. For the first 5 s of the block's motion, find

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 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 particle P is projected vertically upwards with speed $v \mathrm{~m} \mathrm{~s}^{-1}$ from a point on the ground. P reaches its greatest height after 3 s .

A bus moves from rest with constant acceleration for 12 s . It then moves with constant speed for 30 s before decelerating uniformly to rest in a further 6 s . The total distance travelled is 585 m .

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 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.